{"id":"cb_question_bank:a43d8b05-c940-4771-9b4a-c96c643dc5b6","source_id":"cb_question_bank","source_item_id":"a43d8b05-c940-4771-9b4a-c96c643dc5b6","external_id":"2fcb111d-48d0-4ee3-925e-0ffeec3615a4","ibn":null,"question_id":"29e9b28c","program":"SAT","module":"math","domain_code":"S","domain":"Geometry and Trigonometry","skill_code":"S.A.","skill":"Area and volume","difficulty":"E","score_band":2,"answer_type":"mcq","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"The lengths of the sides are x, y, and z. A note indicates the figure is not drawn to scale. The triangle shown has a perimeter of 22 units. If x equals 9 units and y equals 7 units, what is the value of z , in units?","stimulus":"","stimulus_html":null,"stem_html":"

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The triangle shown has a perimeter of 22\n units. If x=9 units and y=7 units, what is the value of z\n, in units?

","rationale_html":"

Choice A is correct. The perimeter of a triangle is the sum of the lengths of its three sides. The triangle shown has side lengths x\n, y\n, and z\n. It's given that the triangle has a perimeter of 22\n units. Therefore, \n\t\n\t\tx\n\t\t+\n\t\ty\n\t\t+\n\t\tz\n\t\n\t=\n\t22\n\n. If \n\tx\n\t=\n\t9\n\n units and \n\ty\n\t=\n\t7\n\n units, the value of z\n, in units, can be found by substituting 9\n for x\n and 7\n for y\n in the equation \n\t\n\t\tx\n\t\t+\n\t\ty\n\t\t+\n\t\tz\n\t\n\t=\n\t22\n\n, which yields 9+7+z=22, or 16+z=22. Subtracting 16\n from both sides of this equation yields \n\tz\n\t=\n\t6\n\n. Therefore, if \n\tx\n\t=\n\t9\n\n units and \n\ty\n\t=\n\t7\n\n units, the value of z\n, in units, is 6\n.

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Choice B is incorrect. This is the value of y\n, in units, not the value of z\n, in units.

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Choice C is incorrect. This is the value of x\n, in units, not the value of z\n, in units.

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Choice D is incorrect. This is the value of \n\tx\n\t+\n\ty\n\n, in units, not the value of z\n, in units.

","correct_answer":["A"],"has_media":true,"has_mathml":true,"has_table":false,"source_created_at":"2023-08-02T20:25:59.836000+00:00","source_updated_at":"2023-08-02T20:25:59.836000+00:00","options":[{"label":"A","content_html":"

6\n

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

7\n

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

9\n

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

16\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}}