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\"}]}"},{"id":2017,"title":"Side of an equilateral triangle","description":"If an equilateral triangle has area A, then what is the length of each of its sides, x?\r\n\r\nImage courtesy of Wikipedia.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 485.5px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 468.5px 242.75px; transform-origin: 468.5px 242.75px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; 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display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"http://upload.wikimedia.org/wikipedia/commons/e/e0/Equilateral-triangle.svg\"\u003e\u003cspan style=\"border-block-end-color: rgb(0, 91, 130); border-block-start-color: rgb(0, 91, 130); border-bottom-color: rgb(0, 91, 130); border-inline-end-color: rgb(0, 91, 130); border-inline-start-color: rgb(0, 91, 130); border-left-color: rgb(0, 91, 130); border-right-color: rgb(0, 91, 130); border-top-color: rgb(0, 91, 130); caret-color: rgb(0, 91, 130); color: rgb(0, 91, 130); column-rule-color: rgb(0, 91, 130); outline-color: rgb(0, 91, 130); text-decoration-color: rgb(0, 91, 130); text-emphasis-color: rgb(0, 91, 130); 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\u003c tolerance)\r\n%%\r\nA = 2;\r\nx_correct = 2*sqrt(2)/sqrt(sqrt(3));\r\ntolerance = 1e-12; \r\nassert(abs(side_length(A) - x_correct) \u003c tolerance)\r\n","published":true,"deleted":false,"likes_count":32,"comments_count":4,"created_by":974,"edited_by":223089,"edited_at":"2026-03-22T08:15:23.000Z","deleted_by":null,"deleted_at":null,"solvers_count":6874,"test_suite_updated_at":"2026-03-22T08:15:23.000Z","rescore_all_solutions":false,"group_id":7,"created_at":"2013-11-27T20:22:35.000Z","updated_at":"2026-04-03T13:42:03.000Z","published_at":"2013-11-28T17:12:13.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document 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this triangle right-angled?","description":"Given three positive numbers a, b, c, where c is the largest number, return true if the triangle with sides a, b and c is right-angled. Otherwise, return false.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 42px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 21px; transform-origin: 407px 21px; vertical-align: baseline; \"\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 233.5px 8px; transform-origin: 233.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGiven three positive numbers a, b, c, where c is the largest number, return\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 14.5px 8px; transform-origin: 14.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003etrue\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 118px 8px; transform-origin: 118px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e if the triangle with sides a, b and c is right-angled. Otherwise, return\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 17px 8px; transform-origin: 17px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003efalse\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function flag = isRightAngled(a, b, c)\r\n  flag = false;\r\nend","test_suite":"%%\r\na = 3;\r\nb = 4;\r\nc = 5;\r\nflag_correct = true;\r\nassert(isequal(isRightAngled(a,b,c),flag_correct))\r\n%%\r\na = 2;\r\nb = 3;\r\nc = 4;\r\nflag_correct = false; \r\nassert(isequal(isRightAngled(a,b,c),flag_correct))\r\n%%\r\na = 5;\r\nb = 12;\r\nc = 13;\r\nflag_correct = true; \r\nassert(isequal(isRightAngled(a,b,c),flag_correct))\r\n\r\n%%\r\na = 17;\r\nb = 19;\r\nc = 23;\r\nflag_correct = false; \r\nassert(isequal(isRightAngled(a,b,c),flag_correct))\r\n\r\n%%\r\na = 12;\r\nb = 35;\r\nc = 37;\r\nflag_correct = true; \r\nassert(isequal(isRightAngled(a,b,c),flag_correct))\r\n\r\n%%\r\na = 10*rand;\r\nb = a;\r\nc = a;\r\nflag_correct = false; \r\nassert(isequal(isRightAngled(a,b,c),flag_correct))","published":true,"deleted":false,"likes_count":38,"comments_count":7,"created_by":974,"edited_by":223089,"edited_at":"2023-05-04T07:40:55.000Z","deleted_by":null,"deleted_at":null,"solvers_count":6416,"test_suite_updated_at":"2023-05-04T07:40:55.000Z","rescore_all_solutions":false,"group_id":7,"created_at":"2013-11-27T20:28:55.000Z","updated_at":"2026-04-02T15:26:12.000Z","published_at":"2013-11-28T17:12:28.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven three positive numbers a, b, c, where c is the largest number, return\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003etrue\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e if the triangle with sides a, b and c is right-angled. Otherwise, return\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003efalse\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":2024,"title":"Triangle sequence ","description":"A sequence of triangles is constructed in the following way:\r\n1) the first triangle is Pythagoras' 3-4-5 triangle\r\n2) the second triangle is a right-angle triangle whose second longest side is the hypotenuse of the first triangle, and whose shortest side is the same length as the second longest side of the first triangle\r\n3) the third triangle is a right-angle triangle whose second longest side is the hypotenuse of the second triangle, and whose shortest side is the same length as the second longest side of the second triangle etc.\r\nEach triangle in the sequence is constructed so that its second longest side is the hypotenuse of the previous triangle and its shortest side is the same length as the second longest side of the previous triangle.\r\nWhat is the area of a square whose side is the hypotenuse of the nth triangle in the sequence?","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 234px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 117px; transform-origin: 407px 117px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 185px 8px; transform-origin: 185px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eA sequence of triangles is constructed in the following way:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 148.5px 8px; transform-origin: 148.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e1) the first triangle is Pythagoras' 3-4-5 triangle\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 365.5px 8px; transform-origin: 365.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e2) the second triangle is a right-angle triangle whose second longest side is the hypotenuse of the first triangle, and whose shortest side is the same length as the second longest side of the first triangle\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 368px 8px; transform-origin: 368px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e3) the third triangle is a right-angle triangle whose second longest side is the hypotenuse of the second triangle, and whose shortest side is the same length as the second longest side of the second triangle etc.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 384px 8px; transform-origin: 384px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eEach triangle in the sequence is constructed so that its second longest side is the hypotenuse of the previous triangle and its shortest side is the same length as the second longest side of the previous triangle.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 299px 8px; transform-origin: 299px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWhat is the area of a square whose side is the hypotenuse of the nth triangle in the sequence?\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function area = triangle_sequence(n)\r\n  area = n;\r\nend","test_suite":"%%\r\nfiletext = fileread('triangle_sequence.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'regexp') || ...\r\n          contains(filetext, 'str2num'); \r\nassert(~illegal)\r\n%%\r\nn = 1;\r\narea_correct = 25;\r\ntolerance = 1e-6;\r\nassert(abs(triangle_sequence(n)-area_correct)\u003ctolerance)\r\n%%\r\nn = 2;\r\narea_correct = 41;\r\ntolerance = 1e-6;\r\nassert(abs(triangle_sequence(n)-area_correct)\u003ctolerance)\r\n%%\r\nn = 3;\r\narea_correct = 66;\r\ntolerance = 1e-6;\r\nassert(abs(triangle_sequence(n)-area_correct)\u003ctolerance)\r\n%%\r\nn = 9;\r\narea_correct = 1186;\r\ntolerance = 1e-6;\r\nassert(abs(triangle_sequence(n)-area_correct)\u003ctolerance)\r\n%%\r\nn = 13;\r\narea_correct = 8129;\r\ntolerance = 1e-6;\r\nassert(abs(triangle_sequence(n)-area_correct)\u003ctolerance)\r\n%%\r\nn = 22;\r\narea_correct = 617911;\r\ntolerance = 1e-6;\r\nassert(abs(triangle_sequence(n)-area_correct)\u003ctolerance)\r\n%%\r\nn = 50;\r\narea_correct = 439116598409;\r\ntolerance = 1e-3;\r\nassert(abs(triangle_sequence(n)-area_correct)\u003ctolerance)","published":true,"deleted":false,"likes_count":156,"comments_count":39,"created_by":974,"edited_by":223089,"edited_at":"2023-03-16T15:12:00.000Z","deleted_by":null,"deleted_at":null,"solvers_count":5829,"test_suite_updated_at":"2023-03-16T15:12:00.000Z","rescore_all_solutions":false,"group_id":7,"created_at":"2013-11-27T20:39:45.000Z","updated_at":"2026-03-31T16:33:25.000Z","published_at":"2013-11-28T17:12:38.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA sequence of triangles is constructed in the following way:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e1) the first triangle is Pythagoras' 3-4-5 triangle\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e2) the second triangle is a right-angle triangle whose second longest side is the hypotenuse of the first triangle, and whose shortest side is the same length as the second longest side of the first triangle\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e3) the third triangle is a right-angle triangle whose second longest side is the hypotenuse of the second triangle, and whose shortest side is the same length as the second longest side of the second triangle etc.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eEach triangle in the sequence is constructed so that its second longest side is the hypotenuse of the previous triangle and its shortest side is the same length as the second longest side of the previous triangle.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWhat is the area of a square whose side is the hypotenuse of the nth triangle in the sequence?\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":2022,"title":"Find a Pythagorean triple","description":"Given four different positive numbers, a, b, c and d, provided in increasing order: a \u003c b \u003c c \u003c d, find if any three of them comprise sides of a right-angled triangle. Return true if they do, otherwise return false .","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 42px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 21px; transform-origin: 407px 21px; vertical-align: baseline; \"\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 376.5px 8px; transform-origin: 376.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGiven four different positive numbers, a, b, c and d, provided in increasing order: a \u0026lt; b \u0026lt; c \u0026lt; d, find if any three of them comprise sides of a right-angled triangle. Return\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 14.5px 8px; transform-origin: 14.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003etrue\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 86px 8px; transform-origin: 86px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e if they do, otherwise return\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 17px 8px; transform-origin: 17px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003efalse\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4px 8px; transform-origin: 4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e .\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function flag = isTherePythagoreanTriple(a, b, c, d)\r\n  flag = false;\r\nend","test_suite":"%%\r\nfiletext = fileread('isTherePythagoreanTriple.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'regexp');\r\nassert(~illegal)\r\n\r\n%%\r\na = 1;\r\nb = 2; \r\nc = 3;\r\nd = 4;\r\nflag_correct = false;\r\nassert(isequal(isTherePythagoreanTriple(a, b, c, d),flag_correct))\r\n%%\r\na = 2;\r\nb = 3; \r\nc = 4;\r\nd = 5;\r\nflag_correct = true;\r\nassert(isequal(isTherePythagoreanTriple(a, b, c, d),flag_correct))\r\n%%\r\na = 3;\r\nb = 4;  \r\nc = 5; \r\nd = 6;\r\nflag_correct = true;\r\nassert(isequal(isTherePythagoreanTriple(a, b, c, d),flag_correct))\r\n%%\r\na = 3;\r\nb = 4; \r\nc = 4.5;\r\nd = 5;\r\nflag_correct = true;\r\nassert(isequal(isTherePythagoreanTriple(a, b, c, d),flag_correct))\r\n%%\r\na = 2;\r\nb = 3;\r\nc = 5;\r\nd = 7;\r\nflag_correct = true;\r\nassert(isequal(isTherePythagoreanTriple(a, b, c, d),~flag_correct))\r\n%%\r\na = 1;\r\nb = 2;\r\nc = sqrt(5);\r\nd = 6;\r\nflag_correct = true;\r\nassert(isequal(isTherePythagoreanTriple(a, b, c, d),flag_correct))\r\n%%\r\na = 5;\r\nb = 7;\r\nc = 12;\r\nd = 13;\r\nflag_correct = true;\r\nassert(isequal(isTherePythagoreanTriple(a, b, c, d),flag_correct))\r\n%%\r\na = 5;\r\nb = 7;\r\nc = 11;\r\nd = 13;\r\nflag_correct = true;\r\nassert(isequal(isTherePythagoreanTriple(a, b, c, d),~flag_correct))","published":true,"deleted":false,"likes_count":48,"comments_count":12,"created_by":974,"edited_by":223089,"edited_at":"2023-03-13T17:24:10.000Z","deleted_by":null,"deleted_at":null,"solvers_count":5084,"test_suite_updated_at":"2023-03-13T17:24:10.000Z","rescore_all_solutions":false,"group_id":7,"created_at":"2013-11-27T20:29:57.000Z","updated_at":"2026-04-02T15:27:25.000Z","published_at":"2013-11-28T17:12:31.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven four different positive numbers, a, b, c and d, provided in increasing order: a \u0026lt; b \u0026lt; c \u0026lt; d, find if any three of them comprise sides of a right-angled triangle. Return\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003etrue\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e if they do, otherwise return\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003efalse\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e .\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":2023,"title":"Is this triangle right-angled?","description":"Given any three positive numbers a, b, c, return true if the triangle with sides a, b and c is right-angled. Otherwise, return false.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 42px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 21px; transform-origin: 407px 21px; vertical-align: baseline; \"\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 381.5px 8px; transform-origin: 381.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGiven any three positive numbers a, b, c, return true if the triangle with sides a, b and c is right-angled. Otherwise, return false.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function flag = isRightAngled(a,b,c)\r\n  flag = false;\r\nend","test_suite":"%%\r\na = 3;\r\nb = 4;\r\nc = 5;\r\nflag_correct = true;\r\nassert(isequal(isRightAngled(a,b,c),flag_correct))\r\n%%\r\na = 3;\r\nb = 4;\r\nc = 6;\r\nflag_correct = false;\r\nassert(isequal(isRightAngled(a,b,c),flag_correct))\r\n%%\r\na = 3;\r\nb = 5;\r\nc = 4; \r\nflag_correct = true;\r\nassert(isequal(isRightAngled(a,b,c),flag_correct))\r\n%%\r\na = 4;\r\nb = 3; \r\nc = 5;\r\nflag_correct = true;\r\nassert(isequal(isRightAngled(a,b,c),flag_correct))\r\n%%\r\na = 4; \r\nb = 5;\r\nc = 3; \r\nflag_correct = true;\r\nassert(isequal(isRightAngled(a,b,c),flag_correct))\r\n%%\r\na = 5; \r\nb = 3;\r\nc = 4; \r\nflag_correct = true;\r\nassert(isequal(isRightAngled(a,b,c),flag_correct))\r\n%%\r\na = 5; \r\nb = 4;\r\nc = 3; \r\nflag_correct = true;\r\nassert(isequal(isRightAngled(a,b,c),flag_correct))\r\n%%\r\na = 5; \r\nb = 12;\r\nc = 13; \r\nflag_correct = true;\r\nassert(isequal(isRightAngled(a,b,c),flag_correct))\r\n%%\r\na = 5; \r\nb = 12;\r\nc = 11; \r\nflag_correct = false;\r\nassert(isequal(isRightAngled(a,b,c),flag_correct))\r\n%%\r\na = 10; \r\nb = 15;\r\nc = 20; \r\nflag_correct = false;\r\nassert(isequal(isRightAngled(a,b,c),flag_correct))","published":true,"deleted":false,"likes_count":38,"comments_count":5,"created_by":974,"edited_by":223089,"edited_at":"2023-01-29T06:52:29.000Z","deleted_by":null,"deleted_at":null,"solvers_count":6563,"test_suite_updated_at":"2023-01-29T06:52:29.000Z","rescore_all_solutions":false,"group_id":7,"created_at":"2013-11-27T20:31:43.000Z","updated_at":"2026-04-03T13:37:50.000Z","published_at":"2013-11-28T17:12:35.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven any three positive numbers a, b, c, return true if the triangle with sides a, b and c is right-angled. Otherwise, return false.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":2019,"title":"Dimensions of a rectangle","description":"The longer side of a rectangle is three times the length of the shorter side. If the length of the diagonal is x, find the width and length of the rectangle.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 42px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 468.5px 21px; transform-origin: 468.5px 21px; vertical-align: baseline; \"\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 21px; text-align: left; transform-origin: 444.5px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 428.625px 8px; transform-origin: 428.625px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe longer side of a rectangle is three times the length of the shorter side. If the length of the diagonal is x, find the width and length of the rectangle.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [width, length] = findRectangleDimensions(x)\r\n  width = x;\r\n  length = x;\r\nend","test_suite":"%%\r\nfiletext = fileread('findRectangleDimensions.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'regexp');\r\nassert(~illegal)\r\n\r\n%%\r\nx = 1\r\nlength_correct = 3/sqrt(10);\r\nwidth_correct = 1/sqrt(10); \r\n[width, length] = findRectangleDimensions(x); \r\ntolerance = 1e-12; \r\nassert( abs(length-length_correct)\u003ctolerance \u0026\u0026 abs(width-width_correct)\u003ctolerance )\r\n\r\n%%\r\nx = 2;\r\nwidth_correct = 2/sqrt(10); \r\nlength_correct = 6/sqrt(10); \r\n[width, length] = findRectangleDimensions(x); \r\ntolerance = 1e-12;\r\nassert(abs(length-length_correct)\u003ctolerance \u0026\u0026 abs(width-width_correct)\u003ctolerance)\r\n","published":true,"deleted":false,"likes_count":49,"comments_count":11,"created_by":974,"edited_by":223089,"edited_at":"2026-03-22T08:23:37.000Z","deleted_by":null,"deleted_at":null,"solvers_count":5781,"test_suite_updated_at":"2026-03-22T08:23:37.000Z","rescore_all_solutions":false,"group_id":7,"created_at":"2013-11-27T20:24:49.000Z","updated_at":"2026-04-03T13:48:18.000Z","published_at":"2013-11-28T17:12:20.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe longer side of a rectangle is three times the length of the shorter side. If the length of the diagonal is x, find the width and length of the rectangle.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":2020,"title":"Area of an Isoceles Triangle","description":"An isosceles triangle has equal sides of length x and a base of length y. Find the area, A, of the triangle. \r\n\r\n\u003c\u003chttps://imgur.com/HVdn9p1.png\u003e\u003e\r\n\r\n\r\nImage courtesy of \u003chttp://upload.wikimedia.org/wikipedia/commons/8/8e/Triangle_isocele.svg Wikipedia\u003e.","description_html":"\u003cp\u003eAn isosceles triangle has equal sides of length x and a base of length y. Find the area, A, of the triangle.\u003c/p\u003e\u003cimg src = \"https://imgur.com/HVdn9p1.png\"\u003e\u003cp\u003eImage courtesy of \u003ca href = \"http://upload.wikimedia.org/wikipedia/commons/8/8e/Triangle_isocele.svg\"\u003eWikipedia\u003c/a\u003e.\u003c/p\u003e","function_template":"function A = isocelesArea(x,y)\r\n  A = \r\nend","test_suite":"%%\r\nx = 5;\r\ny = 8; \r\nA_correct = 12;\r\ntolerance = 1e-12; \r\nassert(abs(isocelesArea(x,y)-A_correct)\u003ctolerance)\r\n%%\r\nx = 2;\r\ny = 2; \r\nA_correct = sqrt(3);\r\ntolerance = 1e-12;\r\nassert(abs(isocelesArea(x,y)-A_correct)\u003ctolerance)\r\n%%\r\nx = 10;\r\ny = 2; \r\nA_correct = sqrt(99);\r\ntolerance = 1e-12; \r\nassert(abs(isocelesArea(x,y)-A_correct)\u003ctolerance)\r\n","published":true,"deleted":false,"likes_count":32,"comments_count":5,"created_by":974,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":6116,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":7,"created_at":"2013-11-27T20:27:15.000Z","updated_at":"2026-04-02T15:30:16.000Z","published_at":"2013-11-28T17:12:24.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/image\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/media/image1.JPEG\"}],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eAn isosceles triangle has equal sides of length x and a base of length y. Find the area, A, of the triangle.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eImage courtesy of\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink 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of a rhombus","description":"If a rhombus has diagonals of length x and x+1, then what is the length of its side, y? \r\n\r\n\u003c\u003chttps://imgur.com/x6hT6mm.png\u003e\u003e\r\n\r\nImage courtesy of \u003chttp://upload.wikimedia.org/wikipedia/commons/b/b5/Rhombus.svg Wikipedia\u003e.","description_html":"\u003cp\u003eIf a rhombus has diagonals of length x and x+1, then what is the length of its side, y?\u003c/p\u003e\u003cimg src = \"https://imgur.com/x6hT6mm.png\"\u003e\u003cp\u003eImage courtesy of \u003ca href = \"http://upload.wikimedia.org/wikipedia/commons/b/b5/Rhombus.svg\"\u003eWikipedia\u003c/a\u003e.\u003c/p\u003e","function_template":"function y = rhombus_side(x)\r\n  y = x;\r\nend","test_suite":"%%\r\nx = 1;\r\ny_correct = sqrt(5)/2;\r\ntolerance = 1e-12; \r\nassert(abs(rhombus_side(x)-y_correct)\u003ctolerance)\r\n%%\r\nx = 3;\r\ny_correct = 5/2;\r\ntolerance = 1e-12; \r\nassert(abs(rhombus_side(x)-y_correct)\u003ctolerance)\r\n%%\r\nx = 2;\r\ny_correct = sqrt(13)/2;\r\ntolerance = 1e-12; 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of an equilateral triangle","description":"If an equilateral triangle has area A, then what is the length of each of its sides, x?\r\n\r\nImage courtesy of Wikipedia.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 485.5px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 468.5px 242.75px; transform-origin: 468.5px 242.75px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; 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display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"http://upload.wikimedia.org/wikipedia/commons/e/e0/Equilateral-triangle.svg\"\u003e\u003cspan style=\"border-block-end-color: rgb(0, 91, 130); border-block-start-color: rgb(0, 91, 130); border-bottom-color: rgb(0, 91, 130); border-inline-end-color: rgb(0, 91, 130); border-inline-start-color: rgb(0, 91, 130); border-left-color: rgb(0, 91, 130); border-right-color: rgb(0, 91, 130); border-top-color: rgb(0, 91, 130); caret-color: rgb(0, 91, 130); color: rgb(0, 91, 130); column-rule-color: rgb(0, 91, 130); outline-color: rgb(0, 91, 130); text-decoration-color: rgb(0, 91, 130); text-emphasis-color: rgb(0, 91, 130); 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\u003c tolerance)\r\n%%\r\nA = 2;\r\nx_correct = 2*sqrt(2)/sqrt(sqrt(3));\r\ntolerance = 1e-12; \r\nassert(abs(side_length(A) - x_correct) \u003c tolerance)\r\n","published":true,"deleted":false,"likes_count":32,"comments_count":4,"created_by":974,"edited_by":223089,"edited_at":"2026-03-22T08:15:23.000Z","deleted_by":null,"deleted_at":null,"solvers_count":6874,"test_suite_updated_at":"2026-03-22T08:15:23.000Z","rescore_all_solutions":false,"group_id":7,"created_at":"2013-11-27T20:22:35.000Z","updated_at":"2026-04-03T13:42:03.000Z","published_at":"2013-11-28T17:12:13.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document 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of an equilateral triangle ","description":"Calculate the area of an equilateral triangle of side x. \r\n\r\n\u003c\u003chttps://i.imgur.com/jlZDHhq.png\u003e\u003e\r\n\r\nImage courtesy of \u003chttp://upload.wikimedia.org/wikipedia/commons/e/e0/Equilateral-triangle.svg Wikipedia\u003e.","description_html":"\u003cp\u003eCalculate the area of an equilateral triangle of side x.\u003c/p\u003e\u003cimg src = \"https://i.imgur.com/jlZDHhq.png\"\u003e\u003cp\u003eImage courtesy of \u003ca href = \"http://upload.wikimedia.org/wikipedia/commons/e/e0/Equilateral-triangle.svg\"\u003eWikipedia\u003c/a\u003e.\u003c/p\u003e","function_template":"function y = equilateral_area(x)\r\n  y = x; \r\nend","test_suite":"%%\r\nx = 1;\r\ny_correct = sqrt(3)/4;\r\ntolerance = 1e-12;\r\nassert(abs(equilateral_area(x)-y_correct)\u003ctolerance)\r\n%%\r\nx = 2;\r\ny_correct = sqrt(3);\r\ntolerance = 1e-12;\r\nassert(abs(equilateral_area(x)-y_correct)\u003ctolerance)\r\n%%\r\nx = 3;\r\ny_correct = sqrt(3)*9/4;\r\ntolerance 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of the hypotenuse","description":"Given short sides of lengths a and b, calculate the length c of the hypotenuse of the right-angled triangle.\r\n\r\n\u003c\u003chttps://i.imgur.com/73mQn4N.png\u003e\u003e\r\n\r\nImage courtesy of \u003chttp://upload.wikimedia.org/wikipedia/commons/7/7c/Right_Angle_Triangle.svg Wikipedia\u003e.","description_html":"\u003cp\u003eGiven short sides of lengths a and b, calculate the length c of the hypotenuse of the right-angled triangle.\u003c/p\u003e\u003cimg src = \"https://i.imgur.com/73mQn4N.png\"\u003e\u003cp\u003eImage courtesy of \u003ca href = \"http://upload.wikimedia.org/wikipedia/commons/7/7c/Right_Angle_Triangle.svg\"\u003eWikipedia\u003c/a\u003e.\u003c/p\u003e","function_template":"function c = hypotenuse(a,b)\r\n  c = \r\nend","test_suite":"%%\r\na = 1;\r\nb = 2; \r\nc_correct = sqrt(5);\r\ntolerance = 1e-12 ; \r\nassert(abs(hypotenuse(a,b)-c_correct)\u003ctolerance);\r\n%%\r\na = 3;\r\nb = 4;\r\nc_correct = 5; \r\ntolerance = 1e-12 ; \r\nassert(abs(hypotenuse(a,b)-c_correct)\u003ctolerance);\r\n%%\r\na = 5;\r\nb = 12;\r\nc_correct = 13; \r\ntolerance = 1e-12 ; \r\nassert(abs(hypotenuse(a,b)-c_correct)\u003ctolerance);\r\n","published":true,"deleted":false,"likes_count":67,"comments_count":9,"created_by":974,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":16508,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":7,"created_at":"2013-11-27T20:11:28.000Z","updated_at":"2026-04-03T18:36:12.000Z","published_at":"2013-11-28T17:12:06.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/image\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/media/image1.png\"}],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml 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\"}]}"},{"id":2024,"title":"Triangle sequence ","description":"A sequence of triangles is constructed in the following way:\r\n1) the first triangle is Pythagoras' 3-4-5 triangle\r\n2) the second triangle is a right-angle triangle whose second longest side is the hypotenuse of the first triangle, and whose shortest side is the same length as the second longest side of the first triangle\r\n3) the third triangle is a right-angle triangle whose second longest side is the hypotenuse of the second triangle, and whose shortest side is the same length as the second longest side of the second triangle etc.\r\nEach triangle in the sequence is constructed so that its second longest side is the hypotenuse of the previous triangle and its shortest side is the same length as the second longest side of the previous triangle.\r\nWhat is the area of a square whose side is the hypotenuse of the nth triangle in the sequence?","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 234px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 117px; transform-origin: 407px 117px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 185px 8px; transform-origin: 185px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eA sequence of triangles is constructed in the following way:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 148.5px 8px; transform-origin: 148.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e1) the first triangle is Pythagoras' 3-4-5 triangle\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 365.5px 8px; transform-origin: 365.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e2) the second triangle is a right-angle triangle whose second longest side is the hypotenuse of the first triangle, and whose shortest side is the same length as the second longest side of the first triangle\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 368px 8px; transform-origin: 368px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e3) the third triangle is a right-angle triangle whose second longest side is the hypotenuse of the second triangle, and whose shortest side is the same length as the second longest side of the second triangle etc.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 384px 8px; transform-origin: 384px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eEach triangle in the sequence is constructed so that its second longest side is the hypotenuse of the previous triangle and its shortest side is the same length as the second longest side of the previous triangle.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 299px 8px; transform-origin: 299px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWhat is the area of a square whose side is the hypotenuse of the nth triangle in the sequence?\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function area = triangle_sequence(n)\r\n  area = n;\r\nend","test_suite":"%%\r\nfiletext = fileread('triangle_sequence.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'regexp') || ...\r\n          contains(filetext, 'str2num'); \r\nassert(~illegal)\r\n%%\r\nn = 1;\r\narea_correct = 25;\r\ntolerance = 1e-6;\r\nassert(abs(triangle_sequence(n)-area_correct)\u003ctolerance)\r\n%%\r\nn = 2;\r\narea_correct = 41;\r\ntolerance = 1e-6;\r\nassert(abs(triangle_sequence(n)-area_correct)\u003ctolerance)\r\n%%\r\nn = 3;\r\narea_correct = 66;\r\ntolerance = 1e-6;\r\nassert(abs(triangle_sequence(n)-area_correct)\u003ctolerance)\r\n%%\r\nn = 9;\r\narea_correct = 1186;\r\ntolerance = 1e-6;\r\nassert(abs(triangle_sequence(n)-area_correct)\u003ctolerance)\r\n%%\r\nn = 13;\r\narea_correct = 8129;\r\ntolerance = 1e-6;\r\nassert(abs(triangle_sequence(n)-area_correct)\u003ctolerance)\r\n%%\r\nn = 22;\r\narea_correct = 617911;\r\ntolerance = 1e-6;\r\nassert(abs(triangle_sequence(n)-area_correct)\u003ctolerance)\r\n%%\r\nn = 50;\r\narea_correct = 439116598409;\r\ntolerance = 1e-3;\r\nassert(abs(triangle_sequence(n)-area_correct)\u003ctolerance)","published":true,"deleted":false,"likes_count":156,"comments_count":39,"created_by":974,"edited_by":223089,"edited_at":"2023-03-16T15:12:00.000Z","deleted_by":null,"deleted_at":null,"solvers_count":5829,"test_suite_updated_at":"2023-03-16T15:12:00.000Z","rescore_all_solutions":false,"group_id":7,"created_at":"2013-11-27T20:39:45.000Z","updated_at":"2026-03-31T16:33:25.000Z","published_at":"2013-11-28T17:12:38.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA sequence of triangles is constructed in the following way:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e1) the first triangle is Pythagoras' 3-4-5 triangle\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e2) the second triangle is a right-angle triangle whose second longest side is the hypotenuse of the first triangle, and whose shortest side is the same length as the second longest side of the first triangle\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e3) the third triangle is a right-angle triangle whose second longest side is the hypotenuse of the second triangle, and whose shortest side is the same length as the second longest side of the second triangle etc.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eEach triangle in the sequence is constructed so that its second longest side is the hypotenuse of the previous triangle and its shortest side is the same length as the second longest side of the previous triangle.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWhat is the area of a square whose side is the hypotenuse of the nth triangle in the sequence?\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":2023,"title":"Is this triangle right-angled?","description":"Given any three positive numbers a, b, c, return true if the triangle with sides a, b and c is right-angled. Otherwise, return false.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 42px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 21px; transform-origin: 407px 21px; vertical-align: baseline; \"\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 381.5px 8px; transform-origin: 381.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGiven any three positive numbers a, b, c, return true if the triangle with sides a, b and c is right-angled. Otherwise, return false.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function flag = isRightAngled(a,b,c)\r\n  flag = false;\r\nend","test_suite":"%%\r\na = 3;\r\nb = 4;\r\nc = 5;\r\nflag_correct = true;\r\nassert(isequal(isRightAngled(a,b,c),flag_correct))\r\n%%\r\na = 3;\r\nb = 4;\r\nc = 6;\r\nflag_correct = false;\r\nassert(isequal(isRightAngled(a,b,c),flag_correct))\r\n%%\r\na = 3;\r\nb = 5;\r\nc = 4; \r\nflag_correct = true;\r\nassert(isequal(isRightAngled(a,b,c),flag_correct))\r\n%%\r\na = 4;\r\nb = 3; \r\nc = 5;\r\nflag_correct = true;\r\nassert(isequal(isRightAngled(a,b,c),flag_correct))\r\n%%\r\na = 4; \r\nb = 5;\r\nc = 3; \r\nflag_correct = true;\r\nassert(isequal(isRightAngled(a,b,c),flag_correct))\r\n%%\r\na = 5; \r\nb = 3;\r\nc = 4; \r\nflag_correct = true;\r\nassert(isequal(isRightAngled(a,b,c),flag_correct))\r\n%%\r\na = 5; \r\nb = 4;\r\nc = 3; \r\nflag_correct = true;\r\nassert(isequal(isRightAngled(a,b,c),flag_correct))\r\n%%\r\na = 5; \r\nb = 12;\r\nc = 13; \r\nflag_correct = true;\r\nassert(isequal(isRightAngled(a,b,c),flag_correct))\r\n%%\r\na = 5; \r\nb = 12;\r\nc = 11; \r\nflag_correct = false;\r\nassert(isequal(isRightAngled(a,b,c),flag_correct))\r\n%%\r\na = 10; \r\nb = 15;\r\nc = 20; \r\nflag_correct = false;\r\nassert(isequal(isRightAngled(a,b,c),flag_correct))","published":true,"deleted":false,"likes_count":38,"comments_count":5,"created_by":974,"edited_by":223089,"edited_at":"2023-01-29T06:52:29.000Z","deleted_by":null,"deleted_at":null,"solvers_count":6563,"test_suite_updated_at":"2023-01-29T06:52:29.000Z","rescore_all_solutions":false,"group_id":7,"created_at":"2013-11-27T20:31:43.000Z","updated_at":"2026-04-03T13:37:50.000Z","published_at":"2013-11-28T17:12:35.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven any three positive numbers a, b, c, return true if the triangle with sides a, b and c is right-angled. Otherwise, return false.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":2022,"title":"Find a Pythagorean triple","description":"Given four different positive numbers, a, b, c and d, provided in increasing order: a \u003c b \u003c c \u003c d, find if any three of them comprise sides of a right-angled triangle. Return true if they do, otherwise return false .","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 42px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 21px; transform-origin: 407px 21px; vertical-align: baseline; \"\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 376.5px 8px; transform-origin: 376.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGiven four different positive numbers, a, b, c and d, provided in increasing order: a \u0026lt; b \u0026lt; c \u0026lt; d, find if any three of them comprise sides of a right-angled triangle. Return\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 14.5px 8px; transform-origin: 14.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003etrue\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 86px 8px; transform-origin: 86px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e if they do, otherwise return\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 17px 8px; transform-origin: 17px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003efalse\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4px 8px; transform-origin: 4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e .\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function flag = isTherePythagoreanTriple(a, b, c, d)\r\n  flag = false;\r\nend","test_suite":"%%\r\nfiletext = fileread('isTherePythagoreanTriple.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'regexp');\r\nassert(~illegal)\r\n\r\n%%\r\na = 1;\r\nb = 2; \r\nc = 3;\r\nd = 4;\r\nflag_correct = false;\r\nassert(isequal(isTherePythagoreanTriple(a, b, c, d),flag_correct))\r\n%%\r\na = 2;\r\nb = 3; \r\nc = 4;\r\nd = 5;\r\nflag_correct = true;\r\nassert(isequal(isTherePythagoreanTriple(a, b, c, d),flag_correct))\r\n%%\r\na = 3;\r\nb = 4;  \r\nc = 5; \r\nd = 6;\r\nflag_correct = true;\r\nassert(isequal(isTherePythagoreanTriple(a, b, c, d),flag_correct))\r\n%%\r\na = 3;\r\nb = 4; \r\nc = 4.5;\r\nd = 5;\r\nflag_correct = true;\r\nassert(isequal(isTherePythagoreanTriple(a, b, c, d),flag_correct))\r\n%%\r\na = 2;\r\nb = 3;\r\nc = 5;\r\nd = 7;\r\nflag_correct = true;\r\nassert(isequal(isTherePythagoreanTriple(a, b, c, d),~flag_correct))\r\n%%\r\na = 1;\r\nb = 2;\r\nc = sqrt(5);\r\nd = 6;\r\nflag_correct = true;\r\nassert(isequal(isTherePythagoreanTriple(a, b, c, d),flag_correct))\r\n%%\r\na = 5;\r\nb = 7;\r\nc = 12;\r\nd = 13;\r\nflag_correct = true;\r\nassert(isequal(isTherePythagoreanTriple(a, b, c, d),flag_correct))\r\n%%\r\na = 5;\r\nb = 7;\r\nc = 11;\r\nd = 13;\r\nflag_correct = true;\r\nassert(isequal(isTherePythagoreanTriple(a, b, c, d),~flag_correct))","published":true,"deleted":false,"likes_count":48,"comments_count":12,"created_by":974,"edited_by":223089,"edited_at":"2023-03-13T17:24:10.000Z","deleted_by":null,"deleted_at":null,"solvers_count":5084,"test_suite_updated_at":"2023-03-13T17:24:10.000Z","rescore_all_solutions":false,"group_id":7,"created_at":"2013-11-27T20:29:57.000Z","updated_at":"2026-04-02T15:27:25.000Z","published_at":"2013-11-28T17:12:31.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven four different positive numbers, a, b, c and d, provided in increasing order: a \u0026lt; b \u0026lt; c \u0026lt; d, find if any three of them comprise sides of a right-angled triangle. Return\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003etrue\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e if they do, otherwise return\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003efalse\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e .\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":2021,"title":"Is this triangle right-angled?","description":"Given three positive numbers a, b, c, where c is the largest number, return true if the triangle with sides a, b and c is right-angled. Otherwise, return false.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 42px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 21px; transform-origin: 407px 21px; vertical-align: baseline; \"\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 233.5px 8px; transform-origin: 233.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGiven three positive numbers a, b, c, where c is the largest number, return\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 14.5px 8px; transform-origin: 14.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003etrue\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 118px 8px; transform-origin: 118px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e if the triangle with sides a, b and c is right-angled. Otherwise, return\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 17px 8px; transform-origin: 17px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003efalse\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function flag = isRightAngled(a, b, c)\r\n  flag = false;\r\nend","test_suite":"%%\r\na = 3;\r\nb = 4;\r\nc = 5;\r\nflag_correct = true;\r\nassert(isequal(isRightAngled(a,b,c),flag_correct))\r\n%%\r\na = 2;\r\nb = 3;\r\nc = 4;\r\nflag_correct = false; \r\nassert(isequal(isRightAngled(a,b,c),flag_correct))\r\n%%\r\na = 5;\r\nb = 12;\r\nc = 13;\r\nflag_correct = true; \r\nassert(isequal(isRightAngled(a,b,c),flag_correct))\r\n\r\n%%\r\na = 17;\r\nb = 19;\r\nc = 23;\r\nflag_correct = false; \r\nassert(isequal(isRightAngled(a,b,c),flag_correct))\r\n\r\n%%\r\na = 12;\r\nb = 35;\r\nc = 37;\r\nflag_correct = true; \r\nassert(isequal(isRightAngled(a,b,c),flag_correct))\r\n\r\n%%\r\na = 10*rand;\r\nb = a;\r\nc = a;\r\nflag_correct = false; \r\nassert(isequal(isRightAngled(a,b,c),flag_correct))","published":true,"deleted":false,"likes_count":38,"comments_count":7,"created_by":974,"edited_by":223089,"edited_at":"2023-05-04T07:40:55.000Z","deleted_by":null,"deleted_at":null,"solvers_count":6416,"test_suite_updated_at":"2023-05-04T07:40:55.000Z","rescore_all_solutions":false,"group_id":7,"created_at":"2013-11-27T20:28:55.000Z","updated_at":"2026-04-02T15:26:12.000Z","published_at":"2013-11-28T17:12:28.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven three positive numbers a, b, c, where c is the largest number, return\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003etrue\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e if the triangle with sides a, b and c is right-angled. Otherwise, return\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003efalse\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":2019,"title":"Dimensions of a rectangle","description":"The longer side of a rectangle is three times the length of the shorter side. If the length of the diagonal is x, find the width and length of the rectangle.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 42px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 468.5px 21px; transform-origin: 468.5px 21px; vertical-align: baseline; \"\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 21px; text-align: left; transform-origin: 444.5px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 428.625px 8px; transform-origin: 428.625px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe longer side of a rectangle is three times the length of the shorter side. If the length of the diagonal is x, find the width and length of the rectangle.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [width, length] = findRectangleDimensions(x)\r\n  width = x;\r\n  length = x;\r\nend","test_suite":"%%\r\nfiletext = fileread('findRectangleDimensions.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'regexp');\r\nassert(~illegal)\r\n\r\n%%\r\nx = 1\r\nlength_correct = 3/sqrt(10);\r\nwidth_correct = 1/sqrt(10); \r\n[width, length] = findRectangleDimensions(x); \r\ntolerance = 1e-12; \r\nassert( abs(length-length_correct)\u003ctolerance \u0026\u0026 abs(width-width_correct)\u003ctolerance )\r\n\r\n%%\r\nx = 2;\r\nwidth_correct = 2/sqrt(10); \r\nlength_correct = 6/sqrt(10); \r\n[width, length] = findRectangleDimensions(x); \r\ntolerance = 1e-12;\r\nassert(abs(length-length_correct)\u003ctolerance \u0026\u0026 abs(width-width_correct)\u003ctolerance)\r\n","published":true,"deleted":false,"likes_count":49,"comments_count":11,"created_by":974,"edited_by":223089,"edited_at":"2026-03-22T08:23:37.000Z","deleted_by":null,"deleted_at":null,"solvers_count":5781,"test_suite_updated_at":"2026-03-22T08:23:37.000Z","rescore_all_solutions":false,"group_id":7,"created_at":"2013-11-27T20:24:49.000Z","updated_at":"2026-04-03T13:48:18.000Z","published_at":"2013-11-28T17:12:20.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe longer side of a rectangle is three times the length of the shorter side. If the length of the diagonal is x, find the width and length of the rectangle.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"}],"no_progress_badge":{"id":53,"name":"Unknown","symbol":"unknown","description":"Partially completed groups","description_html":null,"image_location":"/images/responsive/supporting/matlabcentral/cody/badges/problem_groups_unknown_2.png","bonus":null,"players_count":0,"active":false,"created_by":null,"updated_by":null,"deleted_by":null,"deleted_at":null,"restored_by":null,"restored_at":null,"created_at":"2018-01-10T23:20:29.000Z","updated_at":"2018-01-10T23:20:29.000Z","community_badge_id":null,"award_multiples":false}}