{"id":"cb_practice_pdf:t4-math-m1-q25","source_id":"cb_practice_pdf","source_item_id":"t4-math-m1-q25","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-4","module_number":1,"position":25,"stem":"An isosceles right triangle has a hypotenuse of length 58 inches. What is the perimeter, in inches, of this triangle?","stimulus":"","stimulus_html":null,"stem_html":"<p>An isosceles right triangle has a hypotenuse of length 58 inches. What is the perimeter, in inches, of this triangle?</p>","rationale_html":"<p>Choice C is correct. Since the triangle is an isosceles right triangle, the two sides that form the right angle must be the same length. Let x be the length, in inches, of each of those sides. The Pythagorean theorem states that in a right triangle, 2+ 2= 2 a b c , where c is the length of the hypotenuse and a and b are the lengths of the other two sides. Substituting x for a, x for b, and 58 for c in this 2 +2 =2 2= 2 equation yields x x58 , or 2x 58 . Dividing each side of this equation 2=582 2=2  582 by 2 yields x , or x . Taking the square root of each side of this 2 4 =58 2 =-58 2 equation yields two solutions: x and x . The value of x must be 2 2 =58 2 = positive because it represents a side length. Therefore, x , or x 29 2. 2 + + + The perimeter, in inches, of the triangle is 58 x , oxr 58 2x. Substituting + ( ) 29 2 for x in this expression gives a perimeter, in inches, of 58 2 29 2 , or + 58 58 2. Choice A is incorrect. This is the length, in inches, of each of the congruent sides of the triangle, not the perimeter, in inches, of the triangle. Choice B is incorrect. This is the sum of the lengths, in inches, of the congruent sides of the triangle, not 41 SAT PRACTICE TEST #4 ANSWER EXPLANATIONS SAT ANSWER EXPLANATIONS nnn MATH: MODULE 1 the perimeter, in inches, of the triangle. Choice D is incorrect and may result from conceptual or calculation errors.</p>","correct_answer":["C"],"has_media":false,"has_mathml":false,"has_table":false,"source_created_at":null,"source_updated_at":null,"options":[{"label":"A","content_html":"<p>29 2</p>","ord":0},{"label":"B","content_html":"<p>58 2</p>","ord":1},{"label":"C","content_html":"<p>58 +58 2</p>","ord":2},{"label":"D","content_html":"<p>58 +116 2 ST</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}}