{"id":"cb_question_bank:1326ec1b-a2df-4ef5-9ebd-148d67354150","source_id":"cb_question_bank","source_item_id":"1326ec1b-a2df-4ef5-9ebd-148d67354150","external_id":"bf7a641a-e835-4a95-a957-157c3c91e4ca","ibn":null,"question_id":"1f0b582e","program":"SAT","module":"math","domain_code":"S","domain":"Geometry and Trigonometry","skill_code":"S.A.","skill":"Area and volume","difficulty":"M","score_band":4,"answer_type":"mcq","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"Square X has a side length of 12 centimeters. The perimeter of square Y is 2 times the perimeter of square X. What is the length, in centimeters, of one side of square Y?","stimulus":"","stimulus_html":null,"stem_html":"<p style=\"text-align: left;\">Square X has a side length of <math alttext=\"12\"><mn>12</mn>\n</math> centimeters. The perimeter of square Y is <math alttext=\"2\"><mn>2</mn>\n</math> times the perimeter of square X. What is the length, in centimeters, of one side of square Y?</p>","rationale_html":"<p>Choice D is correct. The perimeter, <math alttext=\"upper P\"><mi>P</mi>\n</math>, of a square can be found using the formula <math alttext=\"upper P equals 4 s\"><mrow>\n\t<mi>P</mi>\n\t<mo>=</mo>\n\t<mrow>\n\t\t<mn>4</mn>\n\t\t<mi>s</mi>\n\t</mrow>\n</mrow>\n</math>, where <math alttext=\"s\"><mi>s</mi>\n</math> is the length of each side of the square. It's given that square X has a side length of <math alttext=\"12\"><mn>12</mn>\n</math> centimeters. Substituting <math alttext=\"12\"><mn>12</mn>\n</math> for <math alttext=\"s\"><mi>s</mi>\n</math> in the formula for the perimeter of a square yields <math alttext=\"upper P equals 4 left parenthesis 12 right parenthesis\"><mi>P</mi><mo>=</mo><mn>4</mn><mfenced><mn>12</mn></mfenced></math>, or <math alttext=\"upper P equals 48\"><mrow>\n\t<mi>P</mi>\n\t<mo>=</mo>\n\t<mn>48</mn>\n</mrow>\n</math>. Therefore, the perimeter of square X is <math alttext=\"48\"><mn>48</mn>\n</math> centimeters. It’s also given that the perimeter of square Y is <math alttext=\"2\"><mn>2</mn>\n</math> times the perimeter of square X. Therefore, the perimeter of square Y is <math alttext=\"2 left parenthesis 48 right parenthesis\"><mn>2</mn><mfenced><mn>48</mn></mfenced></math>, or <math alttext=\"96\"><mn>96</mn>\n</math>, centimeters. Substituting <math alttext=\"96\"><mn>96</mn>\n</math> for <math alttext=\"upper P\"><mi>P</mi>\n</math> in the formula <math alttext=\"upper P equals 4 s\"><mi>P</mi><mo>=</mo><mn>4</mn><mi>s</mi></math> gives <math alttext=\"96 equals 4 s\"><mn>96</mn><mo>=</mo><mn>4</mn><mi>s</mi></math>. Dividing both sides of this equation by <math alttext=\"4\"><mn>4</mn>\n</math> gives <math alttext=\"24 equals s\"><mrow>\n\t<mn>24</mn>\n\t<mo>=</mo>\n\t<mi>s</mi>\n</mrow>\n</math>. Therefore, the length of one side of square Y is <math alttext=\"24\"><mn>24</mn>\n</math> centimeters.</p>\n<p>Choice A is incorrect and may result from conceptual or calculation errors.</p>\n<p>Choice B is incorrect and may result from conceptual or calculation errors.</p>\n<p>Choice C is incorrect and may result from conceptual or calculation errors.</p>","correct_answer":["D"],"has_media":false,"has_mathml":true,"has_table":false,"source_created_at":"2023-08-02T20:25:59.837000+00:00","source_updated_at":"2023-08-02T20:25:59.837000+00:00","options":[{"label":"A","content_html":"<p><math alttext=\"6\"><mn>6</mn>\n</math></p>","ord":0},{"label":"B","content_html":"<p><math alttext=\"10\"><mn>10</mn>\n</math></p>","ord":1},{"label":"C","content_html":"<p><math alttext=\"14\"><mn>14</mn>\n</math></p>","ord":2},{"label":"D","content_html":"<p><math alttext=\"24\"><mn>24</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}}