# The length of the rectangle is 5 times its width. the perimeter of the rectangle is 24 cm.

**The length of the rectangle is 5 times its width. the perimeter of the rectangle is 24 cm. Determine the lengths of the sides of this rectangle.**

Let’s write down the formula for the perimeter of the rectangle. The perimeter of a rectangle is the sum of the length and width of the rectangle multiplied by 2:

P = (a + b) × 2,

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

The problem statement says that the length of the rectangle is 5 times the width. Let us express the length, a, through the width, b:

a = 5 × b.

Substituting the perimeter and the expression for side a into the formula, we solve the equation with one unknown:

24 = (5b + b) × 2.

24 = 6b × 2

24 = 12b

b = 24: 12

b = 2

Side b = 2 cm.Let’s find side a:

a = 5 × 2 = 10 cm.

Answer: the length of the rectangle is 10 cm, the width is 2 cm.