Answer
The length of the side of the square is 6 inches.
The width of the rectangle is 3 inches.
The length of the rectangle is 9 inches.
Work Step by Step
Let X represent the side of the square.
The width of the rectangle is 9 inches less than twice the side of the square. This equals 2X - 9.
The length of the rectangle is 3 inches less than twice the 2 side of the square. This equals 2X - 3.
The perimeter of the square is 4 $\times$ X = 4X.
The formula for the perimeter of the rectangle is width + width + length + length.
The perimeter of the rectangle is: P = 2X - 9 + 2X - 9 + 2X - 3 + 2X - 3 = 8X - 24.
Since their perimeters are equal, we can set up the following equation:
4X = 8X - 24
24 = 4X
Divide both sides by 4.
X = 6
The length of the side of the square is 6.
The width of the rectangle is 2X - 9 = 2 $\times$ 6 - 9 = 3.
The length of the rectangle is 2X - 3 = 2 $\times$ 6 - 3 = 9.
