The perimeters of the square and rectangle are equal. The area of the square is 81 cm.

The perimeters of the square and rectangle are equal. The area of the square is 81 cm. The length of the rectangle is 2 times its width. Find the area of the rectangle.

To solve this problem, remember that the perimeter of a square is equal to the sum of the lengths of all its four sides. Since all sides of a square are equal, its perimeter P = 4a, where a is its side. The area of ​​a square is equal to the square of its side. S = a ^ 2. Find the side of the square.
a = √81 = 9 cm.
Find the perimeter of the square.
P = 4 * 9 = 36 cm.
To solve this problem, recall the formula for the area of ​​a rectangle. The area of ​​the rectangle is equal to the product of the length and the width. S = a * b, where a is the length and b is the width.
The perimeter of a rectangle is the sum of the lengths of all its sides. Since in a rectangle the opposite sides are equal, then P = 2 * (a + b), where a is the length, b is the width. Let the width be x, then the length is 2x.
2 * (x + 2x) = 36
3x = 36/2
3x = 18
x = 18/3
x = 6.
The width is 6 m, the length is 2 * 6 = 12 m. Let’s calculate the area.
S = 6 * 12 = 72 sq.m.
Answer: 72 sq.m.