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

The perimeter 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 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. 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. Let the width be – x cm, then the length is 2x cm. Knowing that the perimeter is 81 cm, we will compose the equation.
2 * (2x + x) = 81;
3x = 81/2;
3x = 40.5;
x = 40.5 / 3;
x = 13.5.
The width is 13.5 cm, and the length is 2 * 13.5 = 27 cm.
Let’s calculate the area.
S = 13.5 * 27 = 364.5 cm ^ 2.
Answer: 364.5 cm ^ 2.