{"id":"cb_question_bank:1f3d49aa-cfa7-4c10-a000-3b71e2f7b76b","source_id":"cb_question_bank","source_item_id":"1f3d49aa-cfa7-4c10-a000-3b71e2f7b76b","external_id":null,"ibn":"021775-DC","question_id":"f89af023","program":"SAT","module":"math","domain_code":"P","domain":"Advanced Math","skill_code":"P.C.","skill":"Nonlinear functions","difficulty":"M","score_band":5,"answer_type":"mcq","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"A rectangular volleyball court has an area of 162 square meters. If the length of the court is twice the width, what is the width of the court, in meters?","stimulus":"","stimulus_html":null,"stem_html":"<p class=\"stem_paragraph \">A rectangular volleyball court has an area of 162&nbsp;square meters. If the length of the court is twice the width, what is the width of the court, in meters?</p>\n","rationale_html":"<p>Choice A is correct. It’s given that the volleyball court is rectangular and has an area of 162 square meters. The formula for the area of a rectangle is <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/04211b45162d91021e6336d42688697b34fc9ca135edde9e7a682f0b2c52a8d4\" alt=\"A equals l w \"></span>, where <span class=\"italic\">A</span> is the area, <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/b3ed61300b239762a0f7bec1dc9a48ecd5e011d08d5338f426429aa3c459a067\" alt=\"l\"></span> is the length, and <span class=\"italic\">w</span> is the width of the rectangle. It’s also given that the length of the volleyball court is twice the width, thus <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/009d1e6a95514f5cfbb1ec21cea9940e3c1b3c3de12635b0253006f98ac883fc\" alt=\"l equals 2 w\"></span>. Substituting the given value into the formula for the area of a rectangle and using the relationship between length and width for this rectangle yields <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/23a58a554235c0550c93a17389ca0eaf005f5efa04cd3280007e7e540f35055b\" alt=\"162 equals, 2 w times w \"></span>. This equation can be rewritten as <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/6deb04c3fdcf68cd4535e8e7768c2b23b87b40da6cad77306e0125acd04f1ec0\" alt=\"162 equals, 2 w squared\"></span>. Dividing both sides of this equation by 2 yields <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/95bf868bbad91966f638f5ed0ef8eb72acf9519fc7998149f5f558406cf61b95\" alt=\"81 equals, w squared\"></span>. Taking the square root of both sides of this equation yields <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/869949d73aa4b738dd452931ad212eb6f0fbc0af19f9c814a6beba8add8cb162\" alt=\"plus or minus 9 equals w\"></span>. Since the width of a rectangle is a positive number, the width of the volleyball court is 9 meters.<br><br>\n\tChoice B is incorrect because this is the length of the rectangle. Choice C is incorrect because this is the result of using 162 as the perimeter rather than the area. Choice D is incorrect because this is the result of calculating <span class=\"italic\">w</span> in the equation <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/74329aa72858a80ac017fcc11049e5b2402b048bd8c42dd63c8baae76eb91a8c\" alt=\"162 equals, 2 w plus w \"></span> instead of <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/e0e3d7fb4162133b132fda94de3e76660eaff3fc9b2ea266561a39fd5c3523a5\" alt=\"162 equals, 2 w times w\"></span>.</p>\n","correct_answer":["A"],"has_media":true,"has_mathml":false,"has_table":false,"source_created_at":"2023-08-02T20:25:59.617000+00:00","source_updated_at":"2023-08-02T20:25:59.617000+00:00","options":[{"label":"A","content_html":"<p class=\"choice_paragraph \">9</p>\n","ord":0},{"label":"B","content_html":"<p class=\"choice_paragraph \">18</p>\n","ord":1},{"label":"C","content_html":"<p class=\"choice_paragraph \">27</p>\n","ord":2},{"label":"D","content_html":"<p class=\"choice_paragraph \">54</p>\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}}