Square P has a side length of x inches. Square Q has a perimeter that is 176 inches greater than

Question

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 ?

Accepted Answer

Choice A is correct. Let x represent the side length, in inches, of square P. It follows that the perimeter of square P is 4 x 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 4 x inches, or 4 x + 176 inches. Since the perimeter of a square is 4 times the side length of the square, each side length of Q is 4 x + 176 4 , or x + 44 inches. Since the area of a square is 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 176 x + 44 inches. Choice D is incorrect. This function represents a square with side lengths 176 x + 176 inches.

Question c99a75