{"id":"cb_practice_pdf:t9-math-m1-q1","source_id":"cb_practice_pdf","source_item_id":"t9-math-m1-q1","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-9","module_number":1,"position":1,"stem":"The lengths of two sides of a triangle are 4 centimeters and 6 centimeters. If the perimeter of the triangle is 18 centimeters, what is the length, in centimeters, of the third side of this triangle?","stimulus":"","stimulus_html":null,"stem_html":"<p>The lengths of two sides of a triangle are 4 centimeters and 6 centimeters. If the perimeter of the triangle is 18 centimeters, what is the length, in centimeters, of the third side of this triangle?</p>","rationale_html":"<p>Choice B is correct. The perimeter of a triangle is the sum of the lengths of all three of its sides. It’s given that the lengths of two sides of a triangle are 4 centimeters and 6 centimeters. Let x represent the length, in centimeters, of the third side of this triangle. The sum of the lengths, in centimeters, of all three 4+6+ sides of the triangle can be represented by the expression x. Since it’s 18 given that the perimeter of the triangle is centimeters, it follows that 4+6+ =18 10+ =18 10 x , or x . Subtracting from both sides of this equation = yields x 8. Therefore, the length, in centimeters, of the third side of this triangle is 8. Choice A is incorrect. If the length of the third side of this triangle were 4+6+2 2 centimeters, the perimeter, in centimeters, of the triangle would be , or 12 18 , not . Choice C is incorrect. If the length of the third side of this triangle were 10 4+6+10 centimeters, the perimeter, in centimeters, of the triangle would be , 20 18 or , not . Choice D is incorrect. If the length of the third side of this triangle 24 were centimeters, the perimeter, in centimeters, of the triangle would be 4+6+24 34 18 , or , not .</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>2</p>","ord":0},{"label":"B","content_html":"<p>8</p>","ord":1},{"label":"C","content_html":"<p>10</p>","ord":2},{"label":"D","content_html":"<p>24</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}}