{"id":"cb_question_bank:f0db7042-55d1-4548-8332-dc1db28dcdb5","source_id":"cb_question_bank","source_item_id":"f0db7042-55d1-4548-8332-dc1db28dcdb5","external_id":null,"ibn":"070630-DC","question_id":"6a3fbec3","program":"SAT","module":"math","domain_code":"S","domain":"Geometry and Trigonometry","skill_code":"S.B.","skill":"Lines, angles, and triangles","difficulty":"H","score_band":7,"answer_type":"spr","answer_source":"rationale","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"In the figure above, the length of line segment B D equals 6 and the length of line segment A D equals 8 . What is the length of line segment D C ?","stimulus":"The figure presents right triangle A B C . Side A C is horizontal, vertex C is to the right of vertex A, vertex B is above side A C , and angle A B C is a right angle. Point D lies on side A C, directly below vertex B, and vertical line segment B D is drawn, dividing triangle A B C into two smaller triangles, triangle A B D and triangle B D C. Angle A D B is a right angle. A note states that the figure is not drawn to scale.","stimulus_html":"<div class=\"stimulus_reference \">\n\t\t\t\t<div class=\"standalone_image \">\n\t\t\t\t\t<img src=\"/api/assets/8a296f1e7bc1743c4ec2c7107eafdc1a1ec965a2305dec43f222add9583ac5ac\" alt=\"The figure presents right triangle A B C . Side A C is horizontal, vertex C is to the right of vertex A, vertex B is above side A C , and angle A B C is a right angle. Point D lies on side A C, directly below vertex B, and vertical line segment B D is drawn, dividing triangle A B C into two smaller triangles, triangle A B D and triangle B D C. Angle A D B is a right angle. A note states that the figure is not drawn to scale.\" width=\"133\" height=\"92\"></div>\n\t\t\t</div>\n","stem_html":"<p class=\"stem_paragraph \">In the figure above, <span class=\"math_expression \">\n\t\t\t\t\t\t<span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/807f3f39b929e7083ebb32ec39dee576837194e37c04b9f2abfca8ca348053fd\" alt=\"the length of line segment B D equals 6\"></span></span> and <span class=\"math_expression \">\n\t\t\t\t\t\t<span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/7ee855c728847797163d97c6a28a3e7eb94176d3f49ecd5f0a7eb8f487f08f62\" alt=\"the length of line segment A D equals 8\"></span></span>. What is the length of <span class=\"math_expression \">\n\t\t\t\t\t\t<span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/bc226a8a529191bf3470637ec35739f13eb9b166440e7f426108a130bca4da25\" alt=\"line segment D C\"></span></span> ?</p>\n","rationale_html":"<p>The correct answer is 4.5. According to the properties of right triangles, <span class=\"italic\">BD</span> divides triangle <span class=\"italic\">ABC</span> into two similar triangles, <span class=\"italic\">ABD</span> and <span class=\"italic\">BCD</span>. The corresponding sides of <span class=\"italic\">ABD</span> and <span class=\"italic\">BCD</span> are proportional, so the ratio of <span class=\"italic\">BD</span> to <span class=\"italic\">AD</span> is the same as the ratio of <span class=\"italic\">DC</span> to <span class=\"italic\">BD</span>. Expressing this information as a proportion gives <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/677a54767244280708497ce9179d62928a98bd0dba3fb9bd382f284b0986d6c3\" alt=\"six eighths equals, the fraction D C, over 6\"></span>. Solving the proportion for <span class=\"italic\">DC</span> results in <span class=\"italic\"></span>\n\t\t\t\t<span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/118b0a7a1d1b0841ccd178a4e6d2c42301289d383f47b8bccdc6b3dd78a5ce04\" alt=\"D C equals 4 point 5\"></span>. Note that 4.5 and 9/2 are examples of ways to enter a correct answer.</p>\n","correct_answer":["4.5"],"has_media":true,"has_mathml":false,"has_table":false,"source_created_at":"2023-08-02T20:25:59.632000+00:00","source_updated_at":"2023-08-02T20:25:59.632000+00:00","options":[],"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}}