The perimeter of a square is twice the perimeter of a rectangle. Given that the rectangle's area is 480 square centimeters, determine the area of the square.

Explanation

Let the side length of the square be 'a' cm, and the rectangle's length and width be 'l' cm and 'b' cm respectively. The perimeter of the square is 4a, and the perimeter of the rectangle is 2(l + b). Given that 4a = 2 × 2(l + b), we get 4a = 4(l + b), so a = l + b. The area of the rectangle is l × b = 480. Since we only know the product l × b and not the sum l + b, we cannot determine the exact value of 'a' or the area of the square (a²). Therefore, the area of the square cannot be determined with the given information.