{"id":"cb_practice_pdf:t10-math-m2-q27","source_id":"cb_practice_pdf","source_item_id":"t10-math-m2-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-10","module_number":2,"position":27,"stem":"- - - -_an_equilateral_triangle_is - - - - - ~ The perimeter of 624 centimeters. The height of this triangle is k 3 centimeters, where k is a constant. What is the value of k? OP","stimulus":"","stimulus_html":null,"stem_html":"<p>- - - -_an_equilateral_triangle_is - - - - - ~ The perimeter of 624 centimeters. The height of this triangle is k 3 centimeters, where k is a constant. What is the value of k? OP</p>","rationale_html":"<p>104 The correct answer is . An equilateral triangle is a triangle in which all three 60° sides have the same length and all three angles have a measure of . The height of the triangle, k 3, is the length of the altitude from one vertex. The altitude divides the equilateral triangle into two congruent 30-60-90 right triangles, where 60° the altitude is the side across from the angle in each 30-60-90 right triangle. Since the altitude has a length of k 3, it follows from the properties of 30° 30-60-90 right triangles that the side across from each angle has a length of k and each hypotenuse has a length of 2k. In this case, the hypotenuse of each 30-60-90 right triangle is a side of the equilateral triangle; therefore, each side length of the equilateral triangle is 2k. The perimeter of a triangle is the sum of the lengths of each side. It’s given that the perimeter of the equilateral triangle 624 2 +2 +2 =624 6 =624 is ; therefore, k k k , or k . Dividing both sides of this =104 equation by 6 yields k . 47 SAT PRACTICE TEST #10 ANSWER EXPLANATIONS</p>","correct_answer":["104"],"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}}