# The length of the rectangle is 5 times its width. Find the area of a rectangle if its perimeter is 156 cm.

1) Find the length and width of the rectangle. We are given a perimeter. The perimeter of a rectangle is the sum of the length and width of the rectangle multiplied by 2. Let’s write the formula:

P = (a + b) × 2,

where a is the length of the rectangle, b is the width.

In the statement of the problem it is said that the length of the rectangle is 5 times greater than the width, which means the width is 5 times less than the length, we write:

b = a / 5.

We substitute the value b in the formula for the perimeter of the rectangle and solve the equation with one unknown:

156 = (a + a / 5) × 2,

156 = 2a + 2a / 5,

156 = 10a / 5 + 2a / 5,

156 = (10a + 2a) / 5,

156 × 5 = 12a,

12a = 780,

a = 65.

This means that the length of the rectangle is 65 cm.Let’s find the width:

b = 65: 5 = 13 cm.

2) Find the area of the rectangle.

The area of a rectangle is the product of the lengths of its sides. Let’s write the formula for the area:

S = a × b,

where a is the length of the rectangle, b is the width.

S = 65 × 13 = 845 cm².

Answer: the area of the rectangle is 845 cm².