{"id":"cb_question_bank:93575bc2-615a-40cb-be17-f4d7a6ae1426","source_id":"cb_question_bank","source_item_id":"93575bc2-615a-40cb-be17-f4d7a6ae1426","external_id":"b479bf47-357b-4283-81e0-02fa0f919256","ibn":null,"question_id":"9ec76b54","program":"SAT","module":"math","domain_code":"S","domain":"Geometry and Trigonometry","skill_code":"S.C.","skill":"Right triangles and trigonometry","difficulty":"M","score_band":4,"answer_type":"mcq","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"A right triangle has legs with lengths of 28 centimeters and 20 centimeters. What is the length of this triangle's hypotenuse, in centimeters?","stimulus":"","stimulus_html":null,"stem_html":"<p style=\"text-align: left;\">A right triangle has legs with lengths of <math alttext=\"28\"><mn>28</mn>\n</math> centimeters and <math alttext=\"20\"><mn>20</mn>\n</math> centimeters. What is the length of this triangle's hypotenuse, in centimeters?</p>","rationale_html":"<p style=\"text-align: left;\">Choice B is correct. The Pythagorean theorem states that in a right triangle, the sum of the squares of the lengths of the two legs is equal to the square of the length of the hypotenuse. It's given that the right triangle has legs with lengths of <math alttext=\"28\"><mn>28</mn>\n</math> centimeters and <math alttext=\"20\"><mn>20</mn>\n</math> centimeters. Let <math alttext=\"c\"><mi>c</mi>\n</math> represent the length of this triangle's hypotenuse, in centimeters. Therefore, by the Pythagorean theorem, <math alttext=\"28 squared plus 20 squared equals c squared\"><msup><mn>28</mn><mn>2</mn></msup><mo>+</mo><msup><mn>20</mn><mn>2</mn></msup><mo>=</mo><msup><mi>c</mi><mn>2</mn></msup></math>, or <math alttext=\"1,184 equals c squared\"><mn>1,184</mn><mo>=</mo><msup><mi>c</mi><mn>2</mn></msup></math>. Taking the positive square root of both sides of this equation yields <math alttext=\"StartRoot 1,184 EndRoot equals c\"><msqrt><mn>1,184</mn></msqrt><mo>=</mo><mi>c</mi></math>, or <math alttext=\"4 StartRoot 74 EndRoot equals c\"><mn>4</mn><msqrt><mn>74</mn></msqrt><mo>=</mo><mi>c</mi></math>. Therefore, the length of this triangle's hypotenuse, in centimeters, is <math alttext=\"4 StartRoot 74 EndRoot\"><mn>4</mn><msqrt><mn>74</mn></msqrt></math>.</p>\n<p style=\"text-align: left;\">Choice A is incorrect and may result from conceptual or calculation errors.</p>\n<p style=\"text-align: left;\">Choice C is incorrect and may result from conceptual or calculation errors.</p>\n<p style=\"text-align: left;\">Choice D is incorrect. This is the square of the length of the triangle’s hypotenuse.</p>","correct_answer":["B"],"has_media":false,"has_mathml":true,"has_table":false,"source_created_at":"2023-08-02T20:25:59.840000+00:00","source_updated_at":"2023-08-02T20:25:59.840000+00:00","options":[{"label":"A","content_html":"<p><math alttext=\"8 StartRoot 6 EndRoot\"><mrow>\n\t<mn>8</mn>\n\t<msqrt>\n\t\t<mn>6</mn>\n\t</msqrt>\n</mrow>\n</math></p>","ord":0},{"label":"B","content_html":"<p><math alttext=\"4 StartRoot 74 EndRoot\"><mrow>\n\t<mn>4</mn>\n\t<msqrt>\n\t\t<mn>74</mn>\n\t</msqrt>\n</mrow>\n</math></p>","ord":1},{"label":"C","content_html":"<p><math alttext=\"48\"><mn>48</mn>\n</math></p>","ord":2},{"label":"D","content_html":"<p><math alttext=\"1,184\"><mn>1,184</mn>\n</math></p>","ord":3}],"attribution":{"source_id":"cb_question_bank","source_name":"College Board digital SAT question bank (community dump)","rights_holder":"College Board","canonical_url":"https://satsuitequestionbank.collegeboard.org/","retrieved_from":"https://raw.githubusercontent.com/mdn522/sat-question-bank/main/data/cb-digital-questions.json","attribution":"SAT practice questions © College Board, from the official SAT Suite Question Bank. Retrieved via the community dump at github.com/mdn522/sat-question-bank.","disclaimer":"SAT® and PSAT/NMSQT® are trademarks registered by the College Board, which is not affiliated with, does not sponsor, and does not endorse this project.","license":"College Board copyright; source repository carries no licence. Local use only.","redistributable":false,"item_count":2017}}