The perimeter of a rectangle is 40 cm. What is the area of this rectangle if its length is 3 times its width?

The perimeter of a rectangle is the sum of its four sides. Moreover, the rectangle has two equal lengths and two equal widths. The sum of the length and width is 40: 2 = 20 (cm).

Let the width be x cm, then the length is 3x cm. The sum of the length and width is (x + 3x) cm or 20 cm. Let’s make an equation and solve it.

x + 3x = 20;

4x = 20;

x = 20: 4;

x = 5 (cm) – the width of the rectangle;

3x = 5 * 3 = 15 (cm) = the length of the rectangle.

The area of the rectangle is equal to the product of the length and the width.

S = 5 * 15 = 75 (cm ^ 2).

Answer. 75 (cm ^ 2).