{"id":"cb_question_bank:bc979c74-87d2-4dfa-a584-4ba351d97752","source_id":"cb_question_bank","source_item_id":"bc979c74-87d2-4dfa-a584-4ba351d97752","external_id":"5466f88b-12d1-4e2d-a8ae-304ba95ffcae","ibn":null,"question_id":"c9f8d1e9","program":"SAT","module":"math","domain_code":"S","domain":"Geometry and Trigonometry","skill_code":"S.C.","skill":"Right triangles and trigonometry","difficulty":"E","score_band":2,"answer_type":"mcq","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"The side lengths are labeled as follows: a b c The angle opposite the side labeled c is a right angle. A note indicates the figure is not drawn to scale. For the right triangle shown, a equals 4 and b equals 5 . Which expression represents the value of c ?","stimulus":"","stimulus_html":null,"stem_html":"

\n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n\n \n \n \n \n \n \n \n \n\n \n\n

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For the right triangle shown, a=4 and b=5. Which expression represents the value of c\n?

","rationale_html":"

Choice D is correct. By the Pythagorean theorem, if a right triangle has a hypotenuse with length c\n and legs with lengths a\n and b\n, then c2=a2+b2. In the right triangle shown, the hypotenuse has length c\n and the legs have lengths a\n and b\n. It's given that a=4 and b=5. Substituting 4\n for a\n and 5\n for b\n in the Pythagorean theorem yields c2=42+52. Taking the square root of both sides of this equation yields c=±42+52. Since the length of a side of a triangle must be positive, the value of c\n is 42+52.

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Choice A is incorrect and may result from conceptual or calculation errors.

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Choice B is incorrect and may result from conceptual or calculation errors.

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Choice C is incorrect and may result from conceptual or calculation errors.

","correct_answer":["D"],"has_media":true,"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":"

4+5

","ord":0},{"label":"B","content_html":"

45

","ord":1},{"label":"C","content_html":"

4+5

","ord":2},{"label":"D","content_html":"

42+52

","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}}