{"id":"cb_question_bank:192bcb7a-635b-41af-b757-ac401ae4eda3","source_id":"cb_question_bank","source_item_id":"192bcb7a-635b-41af-b757-ac401ae4eda3","external_id":null,"ibn":"08390-DC","question_id":"81b664bc","program":"SAT","module":"math","domain_code":"S","domain":"Geometry and Trigonometry","skill_code":"S.B.","skill":"Lines, angles, and triangles","difficulty":"M","score_band":4,"answer_type":"mcq","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"The figure presents quadrilateral A, C D F, where side A, F and side C D are horizontal, and side C D lies above side A, F. Side C D is longer than side A, F. Point B lies on left side A, C, and point E lies on right side D F. Line segment B E, which is horizontal, divides quadrilateral A, C D F into two quadrilaterals, A, B E F and B C D E. In the figure above, side A, F , line segment B E , and side C D are parallel. Points B and E lie on side A, C and side F D , respectively. If the length of line segment A, B equals 9, the length of line segment B C equals 18 point 5 , and the length of line segment F E equals 8 point 5 , what is the length of line segment E D , to the nearest tenth?","stimulus":"","stimulus_html":"<div class=\"stimulus_reference \">\n        <div class=\"standalone_image \"></div>\n      </div>\n","stem_html":"<p><img src=\"/api/assets/2dc5754226f9b1371f5413c5622ddbb2871719cb3966699094586c34ce911270\" alt=\"The figure presents quadrilateral A, C D F, where side A, F and side C D are horizontal, and side C D lies above side A, F. Side C D is longer than side A, F. Point B lies on left side A, C, and point E lies on right side D F. Line segment B E, which is horizontal, divides quadrilateral A, C D F into two quadrilaterals, A, B E F and B C D E.\" width=\"107\" height=\"82\"></p><p class=\"stem_paragraph \">In the figure above, <span class=\"math_expression \"><span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/a26150aa3036148d0c0103afb4d67de3a86a397d1663fcd829f96ebec270d7d3\" alt=\"side A, F \"></span></span>, <span class=\"math_expression \"><span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/8313a0f8199634f3a6b30d6a003dcc9be420cfbba72995f3ce51b6dc34b49f5d\" alt=\"line segment B E \"></span></span>, and <span class=\"math_expression \"><span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/36c6f2b697da9415a19e40b6f9a583ebd96acf07f5d86fae687e1223327789f3\" alt=\"side C D \"></span></span> are parallel. Points <span class=\"italic\">B</span> and <span class=\"italic\">E</span> lie on <span class=\"math_expression \"><span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/838c37eb26f8e7bea94de28d37cede03fda6bc1cb7121288f537103ca3516078\" alt=\"side A, C  \"></span></span> and <span class=\"math_expression \"><span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/8d864192be2907fe89ee3716a5afa7e299d88f911ec7e2d969a9da9d43b325c1\" alt=\"side F D \"></span></span>, respectively. If <span class=\"math_expression \"><span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/8a686c17a930ba430b4803fed69dba0188d2c53c0410e0eafef6b28975add37e\" alt=\"the length of line segment A, B equals 9, the length of line segment B C equals 18 point 5\"></span></span>, and <span class=\"math_expression \"><span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/f43180e0db73340cc9c58f1998b3a636c0c60aefc6430113fc03ecf319f4bfa6\" alt=\"the length of line segment F E equals 8 point 5\"></span></span>, what is the length of <span class=\"math_expression \"><span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/ce27494cba21070765f608640c4acc25a3654d570274d4a554b13a1a5bbdb59b\" alt=\"line segment E D \"></span></span>, to the nearest tenth?</p><p></p>\n","rationale_html":"<p>Choice B is correct. Since <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/a4758f4a0c9cbd08977c495fad11fe991201975944480b842c86bbc47215191d\" alt=\"line segment A F\"></span>, <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/191b065c6fc914e655e98180ba2c76d448565f068749e6a5ee63836e022e3608\" alt=\"line segment B E\"></span>, and <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/911a7d048cdb0ea8f0f468b54e5c2231761970fa761739951e39d2f9fed4190e\" alt=\"line segment C D \"></span> are parallel, quadrilaterals <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/8d9fef23bc2b0c720a808610e0f7b7d64eb5bf87eae87ec9860c6f82a13e0501\" alt=\"A F E B \"></span> and <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/f4b67f9147026ca2faf8ca6e55a1afefafdd34d3d349b656df582880a813a506\" alt=\"B E D C \"></span> are similar. Let <span class=\"italic\">x</span> represent the length of <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/ce27494cba21070765f608640c4acc25a3654d570274d4a554b13a1a5bbdb59b\" alt=\"line segment E D\"></span>. With similar figures, the ratios of the lengths of corresponding sides are equal. It follows that <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/d346cf571f478d1406393cd6264c0199557aa2f4e8d60e5aaec39380e53cf8aa\" alt=\"9 over 18 point 5, equals 8 point 5 over x\"></span>. Multiplying both sides of this equation by 18.5 and by <span class=\"italic\">x</span> yields <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/fe13dc3f10204a6f7919da03fe1a7760d16d8dc9ad518f0bd898a93345c193ee\" alt=\"9 x equals, 18 point 5, times 8 point 5\"></span>, or <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/4a0eebb6339eb07ec6460c200fa0d608bcf1cfaed4469dd081c3e45e8c658064\" alt=\"9 x equals 157 point 2 5\"></span>. Dividing both sides of this equation by 9 yields <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/1e75fb4e295a4900ce874ad4e3fa5d121ab5c5eda697a93d8ccfe6229adca3a0\" alt=\"x equals 17 point 4 7\"></span>, which to the nearest tenth is 17.5.</p><p>Choices A, C, and D are incorrect and may result from errors made when setting up the proportion.</p><p></p>\n","correct_answer":["B"],"has_media":true,"has_mathml":false,"has_table":false,"source_created_at":"2023-08-02T20:25:59.636000+00:00","source_updated_at":"2023-08-02T20:25:59.636000+00:00","options":[{"label":"A","content_html":"<p class=\"choice_paragraph \">16.8</p>\n","ord":0},{"label":"B","content_html":"<p class=\"choice_paragraph \">17.5</p>\n","ord":1},{"label":"C","content_html":"<p class=\"choice_paragraph \">18.4</p>\n","ord":2},{"label":"D","content_html":"<p class=\"choice_paragraph \">19.6</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}}