{"id":"cb_question_bank:bccb6500-2979-4783-a862-979a7e0050c4","source_id":"cb_question_bank","source_item_id":"bccb6500-2979-4783-a862-979a7e0050c4","external_id":"2cc3f845-5222-4c22-8764-9d19c7b188fb","ibn":null,"question_id":"f60bb551","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 area of a rectangle is 630 square inches. The length of the rectangle is 70 inches. What is the width, in inches, of this rectangle?","stimulus":"","stimulus_html":null,"stem_html":"<p style=\"text-align: left;\">The area of a rectangle is <math alttext=\"630\"><mn>630</mn>\n</math> square inches. The length of the rectangle is <math alttext=\"70\"><mn>70</mn>\n</math> inches. What is the width, in inches, of this rectangle?</p>","rationale_html":"<p style=\"text-align: left;\">Choice A is correct. The area <math alttext=\"upper A\"><mi>A</mi>\n</math>, in square inches, of a rectangle is the product of its length <math alttext=\"script l\"><mi>l</mi></math>, in inches, and its width <math alttext=\"w\"><mi>w</mi>\n</math>, in inches; thus, <math alttext=\"upper A equals script l w\"><mi>A</mi><mo>=</mo><mi>l</mi><mi>w</mi></math>. It's given that the area of a rectangle is <math alttext=\"630\"><mn>630</mn>\n</math> square inches and the length of the rectangle is <math alttext=\"70\"><mn>70</mn>\n</math> inches. Substituting <math alttext=\"630\"><mn>630</mn>\n</math> for <math alttext=\"upper A\"><mi>A</mi>\n</math> and <math alttext=\"70\"><mn>70</mn>\n</math> for&nbsp;<math alttext=\"script l\"><mi>l</mi></math> in the equation&nbsp;<math alttext=\"upper A equals script l w\"><mi>A</mi><mo>=</mo><mi>l</mi><mi>w</mi></math> yields <math alttext=\"630 equals 70 w\"><mrow>\n\t<mn>630</mn>\n\t<mo>=</mo>\n\t<mrow>\n\t\t<mn>70</mn>\n\t\t<mi>w</mi>\n\t</mrow>\n</mrow>\n</math>. Dividing both sides of this equation by <math alttext=\"70\"><mn>70</mn>\n</math> yields <math alttext=\"9 equals w\"><mrow>\n\t<mn>9</mn>\n\t<mo>=</mo>\n\t<mi>w</mi>\n</mrow>\n</math>. Therefore, the width, in inches, of this rectangle is <math alttext=\"9\"><mn>9</mn>\n</math>.</p>\n<p style=\"text-align: left;\">Choice B is incorrect. This is the length, not the width, in inches, of the rectangle.</p>\n<p style=\"text-align: left;\">Choice C is incorrect. This is half the area, in square inches, not the width, in inches, of the rectangle.</p>\n<p style=\"text-align: left;\">Choice D is incorrect. This is the difference between the area, in square inches, and the length, in inches, of the rectangle, not the width, in inches, of the rectangle.</p>","correct_answer":["A"],"has_media":false,"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":"<p><math alttext=\"9\"><mn>9</mn>\n</math></p>","ord":0},{"label":"B","content_html":"<p><math alttext=\"70\"><mn>70</mn>\n</math></p>","ord":1},{"label":"C","content_html":"<p><math alttext=\"315\"><mn>315</mn>\n</math></p>","ord":2},{"label":"D","content_html":"<p><math alttext=\"560\"><mn>560</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}}