# The perimeter of the square is equal to the perimeter of the rectangle. Square area 81 cm2.

**The perimeter of the square is equal to the perimeter of the rectangle. Square area 81 cm2. The length of the rectangle is 2 times longer than the width. Find the area of a rectangle**

1. Find the side of the square, for this we extract the square root from the value of the area.

√81 = 9 (cm) side of the square.

2. Find the perimeter of the square by multiplying the length of its side by the number of sides since they are equal in the square.

9 * 4 = 36 (cm) perimeter of the square.

3. Let the width of the rectangle be x cm, then the length of the rectangle is 2 * x = (2x) cm.

Find the semi-perimeter of the rectangle x + 2x = (3x) cm, and by condition, the semi-perimeter.

36/2 = 18 (cm).

Let’s compose and solve the equation.

3x = 18;

x = 18/3;

x = 6 cm width of the rectangle, then the length is 6 * 2 = 12 cm.

4. Find the area of the rectangle by multiplying the length by the width.

6 * 12 = 72 (cm2).

Answer: 72 cm2.