OG详解-OG4 数学1 Q18

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 side length of Q is  4x+1764​​, 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 (x + 44)(x + 44), or (x + 44⁾² square inches. It follows that function f is defined by f (x)=(x + 44)² .
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.