{"id":"cb_practice_pdf:t8-math-m1-q27","source_id":"cb_practice_pdf","source_item_id":"t8-math-m1-q27","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":"spr","answer_source":"rationale","layout_warning":"Part of this question was typeset outside the text flow — a fraction, subscript or similar — and PDF extraction re-inserted it in the wrong place. The wording is reliable; the symbols may be out of order.","form_id":"cb_practice_pdf:test-8","module_number":1,"position":27,"stem":"The perimeter of an equilateral triangle is 852 centimeters. The three vertices of the triangle lie on a circle. The radius of the circle is w 3 centimeters. What is the value of w? OP","stimulus":"","stimulus_html":null,"stem_html":"<p>The perimeter of an equilateral triangle is 852 centimeters. The three vertices of the triangle lie on a circle. The radius of the circle is w 3 centimeters. What is the value of w? OP</p>","rationale_html":"<p>284 The correct answer is 3 . Since the perimeter of a triangle is the sum of the lengths of its sides, and the given triangle is equilateral, the length of each side is 852 284 3 , or , centimeters (cm). Right triangle AMO can be formed, where M is the midpoint of one of the triangle’s sides, A is one of this side’s endpoints, and O is 284 142 the center of the circle. It follows that AM is 2 , or , cm. Additionally, 30c 60c 90c triangle AMO has angles measuring , , and , where the measure of 90c 30c angle OMA is and the measure of angle OAM is . It follows that the length 39 SAT PRACTICE TEST #8 ANSWER EXPLANATIONS SAT ANSWER EXPLANATIONS n MATH: MODULE 1 of side MO is half the length of hypotenuse AO, and the length of side AM is = 3 times the length of side MO. It’s given that AO w 3 cm. Therefore, 3 3 3 3 MO =w 2 cm and AM =w 2 cm, which is equivalent to AM = 2w cm. Since AM =142 cm, it follows that 3 2w=142 . Multiplying both sides of this equation by 2 3 =284 = 284 yields w . Dividing both sides of this equation by 3 yields w 3 . Note that 284/3, 94.66, and 94.67 are examples of ways to enter a correct answer. 40 SAT PRACTICE TEST #8 ANSWER EXPLANATIONS</p>","correct_answer":["3"],"has_media":false,"has_mathml":false,"has_table":false,"source_created_at":null,"source_updated_at":null,"options":[],"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}}