Question

Pierre folded a square piece of paper vertically to make two rectangles. Each rectangle had a perimeter of 39 inches. How long is each side of the original square? What is the area of the original square? What is the area of one of the rectangles?

Answer 1

Answer:

Each side of the square is 13 inches long. The area of the original square is 169 square inches. The area of one of the rectangles is 84.5 square inches.

Step-by-step explanation:

The shorter side of the rectangle is named as X and the longer side is 2X because the piece of paper is folded in half.

So the perimeter of one of the rectangles is given by the following equation:

$P_{Rectangle}=2(X)+2(2X)=39 in$

So we can find X by solving this equation:

2X+4X=39 in

6X=39 in

X=39 in ÷ 6

X=6.5 in

The sides of the square are equal to 2X, so, each side of the square is 13 in.

The area of the square is given by:

$A_{Square}=(2X)^{2} =(13 in)^{2} =169in^2$

The area of one of the rectangles is given by:

$A_{Rectangle}=X*2X =(6.5 in)* (13 in) =84.5in^2$