{"id":"cb_question_bank:754ec0bb-d2e3-43fe-b439-4895d3800c42","source_id":"cb_question_bank","source_item_id":"754ec0bb-d2e3-43fe-b439-4895d3800c42","external_id":null,"ibn":"025774-DC","question_id":"0837c3b9","program":"SAT","module":"math","domain_code":"S","domain":"Geometry and Trigonometry","skill_code":"S.A.","skill":"Area and volume","difficulty":"E","score_band":3,"answer_type":"mcq","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"Triangle ABC and triangle DEF are similar triangles, where line segment A B and line segment D E are corresponding sides. If the length of line segment D E equals, 2 times the length of line segment A B and the perimeter of triangle ABC is 20, what is the perimeter of triangle DEF ?","stimulus":"","stimulus_html":null,"stem_html":"<p class=\"stem_paragraph \">Triangle <span class=\"italic\">ABC</span> and triangle <span class=\"italic\">DEF</span> are similar triangles, where <span class=\"math_expression \"><span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/bc38232964225d3fa314e7d0470d11422beea36b6598d546923dc085e690921c\" alt=\"line segment A B\"></span></span> and <span class=\"math_expression \"><span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/a52774021adb8f06dd866b688c6a0dd3fada4d7dff553049a2b2030c4632a27b\" alt=\"line segment D E \"></span></span> are corresponding sides. If <span class=\"math_expression \"><span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/85c503b31491607b188fdde37c0ffdf2cb3a8a3407d68f68593e342a6ca12d7e\" alt=\"the length of line segment D E equals, 2 times the length of line segment A B \"></span></span> and the perimeter of triangle <span class=\"italic\">ABC</span> is 20, what is the perimeter of triangle <span class=\"italic\">DEF </span>?</p>\n","rationale_html":"<p>Choice B is correct. Since triangles <span class=\"italic\">ABC</span> and <span class=\"italic\">DEF</span> are similar and <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/85c503b31491607b188fdde37c0ffdf2cb3a8a3407d68f68593e342a6ca12d7e\" alt=\"the length of side D E equals, 2 times the length of side A B\"></span>, the length of each side of triangle <span class=\"italic\">DEF</span> is two times the length of its corresponding side in triangle <span class=\"italic\">ABC</span>. Therefore, the perimeter of triangle <span class=\"italic\">DEF</span> is two times the perimeter of triangle <span class=\"italic\">ABC</span>. Since the perimeter of triangle <span class=\"italic\">ABC</span> is 20, the perimeter of triangle <span class=\"italic\">DEF</span> is 40.</p><p>Choice A is incorrect. This is half, not two times, the perimeter of triangle <span class=\"italic\">ABC</span>. Choice C is incorrect. This is two times the perimeter of triangle <span class=\"italic\">DEF</span> rather than two times the perimeter of triangle <span class=\"italic\">ABC</span>. Choice D is incorrect. This is six times, not two times, the perimeter of triangle <span class=\"italic\">ABC</span>.</p><p></p>\n","correct_answer":["B"],"has_media":true,"has_mathml":false,"has_table":false,"source_created_at":"2023-08-02T20:25:59.619000+00:00","source_updated_at":"2023-08-02T20:25:59.619000+00:00","options":[{"label":"A","content_html":"<p class=\"choice_paragraph \">10</p>\n","ord":0},{"label":"B","content_html":"<p class=\"choice_paragraph \">40</p>\n","ord":1},{"label":"C","content_html":"<p class=\"choice_paragraph \">80</p>\n","ord":2},{"label":"D","content_html":"<p class=\"choice_paragraph \">120</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}}