{"id":"cb_question_bank:7d93ab48-f21d-4f63-809d-054c50ef9739","source_id":"cb_question_bank","source_item_id":"7d93ab48-f21d-4f63-809d-054c50ef9739","external_id":"16428dd4-6b32-4580-ace2-d2dbf0505a76","ibn":null,"question_id":"568d66a7","program":"SAT","module":"math","domain_code":"S","domain":"Geometry and Trigonometry","skill_code":"S.C.","skill":"Right triangles and trigonometry","difficulty":"H","score_band":7,"answer_type":"mcq","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"An isosceles right triangle has a perimeter of 94 plus 94 StartRoot 2 EndRoot inches. What is the length, in inches, of one leg of this triangle?","stimulus":"","stimulus_html":null,"stem_html":"

An isosceles right triangle has a perimeter of \n\t94\n\t+\n\t\n\t\t94\n\t\t\n\t\t\t2\n\t\t\n\t\n\n inches. What is the length, in inches, of one leg of this triangle?

","rationale_html":"

Choice B is correct. It's given that the right triangle is isosceles. In an isosceles right triangle, the two legs have equal lengths, and the length of the hypotenuse is \n\t2\n\n times the length of one of the legs. Let l represent the length, in inches, of each leg of the isosceles right triangle. It follows that the length of the hypotenuse is l2 inches. The perimeter of a figure is the sum of the lengths of the sides of the figure. Therefore, the perimeter of the isosceles right triangle is l+l+l2 inches. It's given that the perimeter of the triangle is 94+942 inches. It follows that l+l+l2=94+942. Factoring the left-hand side of this equation yields 1+1+2l=94+942, or 2+2l=94+942. Dividing both sides of this equation by 2+2 yields l=94+9422+2. Rationalizing the denominator of the right-hand side of this equation by multiplying the right-hand side of the equation by 2-22-2 yields l=94+9422-22+22-2. Applying the distributive property to the numerator and to the denominator of the right-hand side of this equation yields l=188-942+1882-9444-22+22-4. This is equivalent to l=9422, or l=472. Therefore, the length, in inches, of one leg of the isosceles right triangle is \n\t47\n\t\n\t\t2\n\t\n\n.

\n

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

\n

Choice C is incorrect. This is the length, in inches, of the hypotenuse.

\n

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

","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":"

47\n

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

\n\t47\n\t\n\t\t2\n\t\n\n

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

94\n

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

\n\t94\n\t\n\t\t2\n\t\n\n

","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}}