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?
Correct answer: A (parsed from the explanation — this source omits an answer key for this item)
Explanation
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.
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