{"id":"cb_practice_pdf:t7-math-m2-q24","source_id":"cb_practice_pdf","source_item_id":"t7-math-m2-q24","external_id":null,"ibn":null,"question_id":null,"program":"SAT","module":"math","domain_code":null,"domain":null,"skill_code":null,"skill":null,"difficulty":null,"score_band":null,"answer_type":"mcq","answer_source":"rationale","layout_warning":null,"form_id":"cb_practice_pdf:test-7","module_number":2,"position":24,"stem":"XYZ In triangle, angle Z is a right angle and the tanX = length of YZ is 24 units. If 12/35, what is the perimeter, in units, of triangle XYZ?","stimulus":"","stimulus_html":null,"stem_html":"<p>XYZ In triangle, angle Z is a right angle and the tanX = length of YZ is 24 units. If 12/35, what is the perimeter, in units, of triangle XYZ?</p>","rationale_html":"<p>Choice B is correct. It’s given that angle Z in triangle XYZ is a right angle. Thus, side YZ is the leg opposite angle X and side XZ is the leg adjacent to angle X. The tangent of an acute angle in a right triangle is the ratio of the length of the leg opposite the angle to the length of the leg adjacent to the angle. It follows that tan X =YZ . It’s given that tan X = 3 1 5 2 and the length of side YZ is 24 units. Substitu X ti Z ng 3 1 5 2 for tan X and 24 for YZ in the equation tan X =YZ yields 3 1 5 2 = 24 . XZ XZ 35 12 =24 35 Multiplying both sides of this equation by ^XZh yields ^XZh ^ h, or 12 =840 12 =70 ^XZh . Dividing both sides of this equation by yields XZ . The length XY can be calculated using the Pythagorean theorem, which states that if a right triangle has legs with lengths of a and b and a hypotenuse with length c, 2+ 2= 2 70 24 then a b c . Substituting for a and for b in this equation yields 702+242= 2 5,476= 2 c , or c . Taking the square root of both sides of this equation !74= 74= yields c. Since the length of the hypotenuse must be positive, c. 74 Therefore, the length of XY is units. The perimeter of a triangle is the sum of 74+70+24 168 the lengths of all sides. Thus, ^ h units, or units, is the perimeter of triangle XYZ. Choice A is incorrect and may result from conceptual or calculation errors. Choice C is incorrect. This would be the perimeter, in units, for a right triangle 12 24 where the length of side YZ is units, not units. Choice D is incorrect and may result from conceptual or calculation errors.</p>","correct_answer":["B"],"has_media":false,"has_mathml":false,"has_table":false,"source_created_at":null,"source_updated_at":null,"options":[{"label":"A","content_html":"<p>188</p>","ord":0},{"label":"B","content_html":"<p>168</p>","ord":1},{"label":"C","content_html":"<p>84</p>","ord":2},{"label":"D","content_html":"<p>71</p>","ord":3}],"attribution":{"source_id":"cb_practice_pdf","source_name":"College Board full-length SAT practice tests (PDF)","rights_holder":"College Board","canonical_url":"https://satsuite.collegeboard.org/practice/practice-tests/paper","retrieved_from":"https://satsuite.collegeboard.org/practice/practice-tests/paper","attribution":"Full-length SAT practice tests 4–11 © College Board, published free at satsuite.collegeboard.org.","disclaimer":"Extracted from PDF layout: equations, figures and tables do not survive intact. Use the original PDFs for anything the text renders poorly. SAT® is a trademark registered by the College Board, which is not affiliated with and does not endorse this project.","license":"College Board copyright. Free to download; not licensed for redistribution.","redistributable":false,"item_count":905}}