{"id":"cb_practice_pdf:t4-math-m1-q18","source_id":"cb_practice_pdf","source_item_id":"t4-math-m1-q18","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":18,"stem":"Square P has a side length of x inches. Square Q has a perimeter that is 176 inches greater than the perimeter of square P. The function f gives the area of square Q, in square inches. Which of the following defines f?","stimulus":"","stimulus_html":null,"stem_html":"<p>Square P has a side length of x inches. Square Q has a perimeter that is 176 inches greater than the perimeter of square P. The function f gives the area of square Q, in square inches. Which of the following defines f?</p>","rationale_html":"<p>Choice A is correct. Let x represent the side length, in inches, of square P. It follows that the perimeter of square P is 4x inches. It’s given that square Q has a perimeter that is 176 inches greater than the perimeter of square P. Thus, the + perimeter of square Q is 176 inches greater than 4x inches, or 4x 176 inches. Since the perimeter of a square is 4 times the side length of the square, each 4x + 176 + side length of Q is , or x 44 inches. Since the area of a square is 4 calculated by multiplying the length of two sides, the area of square Q is ( )(+ ) + ( + )2 44x 44x, or x 44 square inches. It follows that function f is defined ( ) (= +)2 by f x x 44 . Choice B is incorrect. This function represents a square with side lengths ( + ) x 176 inches. Choice C is incorrect. This function represents a square with ( + ) side lengths 176x 44 inches. Choice D is incorrect. This function represents a ( + ) square with side lengths 176x 176 inches.</p>","correct_answer":["A"],"has_media":false,"has_mathml":false,"has_table":false,"source_created_at":null,"source_updated_at":null,"options":[{"label":"A","content_html":"<p>f(x ) = (x+ 44)^2</p>","ord":0},{"label":"B","content_html":"<p>f(x ) = (x+ 176)^2</p>","ord":1},{"label":"C","content_html":"<p>f(x ) = (176x+ 44)^2</p>","ord":2},{"label":"D","content_html":"<p>f(x ) = (176x+ 176)^2</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}}