A square piece of cloth is folded in half to form a rectangle. If the resulting rectangle has a perimeter of 8 inches, what are the area and perimeter of the square piece of cloth?

2 L + 2 (L/2) = 8

L = 8/3
area = 64/9
perimeter = 4 L = 32/3

To solve this problem, we need to understand the relationship between the square cloth and the resulting rectangle when it is folded in half.

Let's assume the side length of the square piece of cloth is "s" inches. When it is folded in half, the resulting rectangle will have one side with a length of "s" inches, while the other side will have a length of "s/2" inches.

Now, we are given that the perimeter of the resulting rectangle is 8 inches. The perimeter of a rectangle is given by the formula P = 2(length + width). In this case, the perimeter is equal to 8 inches, so we can write the following equation:

8 = 2(s + s/2)

Simplifying the equation:

8 = 2(3s/2)
4 = 3s/2

To isolate "s," we can multiply both sides of the equation by 2/3:

s = (4)(2/3)
s = 8/3

So, the side length of the square piece of cloth is 8/3 inches.

Now, we can find the area and perimeter of the square piece of cloth.

The area of a square is given by the formula A = s^2, where "s" is the side length. Substituting in the value we found for "s":

A = (8/3)^2
A = 64/9 square inches

The perimeter of a square is given by the formula P = 4s. Substituting in the value we found for "s":

P = 4(8/3)
P = 32/3 inches

Therefore, the area of the square piece of cloth is 64/9 square inches, and the perimeter is 32/3 inches.