# Perimeter of Rectangle – Definition with Examples

## Perimeter of Rectangle

The perimeter of a two-dimensional shape is the total length of the outline. To find the perimeter of a rectangle, we add the lengths of all four sides. Since opposite sides of a rectangle are always equal, we need to find the dimensions of length and width to find the perimeter of a rectangle. We can write the perimeter of the rectangle as twice the sum of its length and width. The perimeter is a linear measure and has units as meters, centimeters, inches, feet, etc.

## Formula for the Perimeter of a Rectangle

The letter ‘P’ denotes the perimeter of a rectangle. Let l denote the length and w denote the width of the rectangle. The perimeter (P) of a rectangle is the total length of all the sides of the rectangle. Since the opposite sides of a rectangle are equal, a rectangle has two equal lengths and two equal widths.

The formula for the perimeter of a rectangle is given below:

Perimeter = length + length + width + width

P = l + l + w + w

Or, P = 2 (l + w)

Hence, the formula for the perimeter of a rectangle, P = 2 × (length + width) = 2 × (sum of adjacent sides)

## Real-World Applications

• To find out the distance covered by walking around a rectangular park.
• To measure the length of barbed wire required to create a fence around a rectangular plot of land.
• To draw a border with limestone around a rectangular ground and determine how much limestone would be required to mark the ground’s total periphery.

## Solved Examples

1. The length of a rectangle is 25 cm and the width is 4 cm. What is the perimeter of this rectangle?

Solution:

Length of the rectangle, l = 25 cm

Width of the rectangle, w = 4 cm

Perimeter of the rectangle, P = 2 (l + w) = 2 (25 + 4) = 58

The perimeter of the given rectangle is 58 cm.

1. The length of a rectangular yard is 10 m more than the width. If the yard’s length is 25 m, find the perimeter of this rectangular yard?

Solution:

The length of the rectangular yard is 10 m more than the width. Since the length of the yard is 25 m, the width of this rectangular yard is 25 m – 10 m or 15 m.

Length of the yard, l = 25 m

Width of the yard, w = 15 m

Perimeter, P = 2 (l + w) = 2 (25 + 15) = 2 (40) = 80

The perimeter of the given rectangle is 80 m.

1. The perimeter of a rectangle is 100 cm. The length of this rectangle is 35 cm. Calculate the width of the rectangle.

Solution:

Using the formula P = 2 (l + w), we can say that 2 (35 + w) = 100

Or, 35 + w = 1002  = 50

Therefore w = 50 – 35 = 15

The width of the given rectangle is 15 cm.

## Practice Problems

### 1The perimeter of a rectangle is 150 cm, and the width is 20 cm. What is the length of this rectangle?

40 cm
45 cm
50 cm
55 cm
CorrectIncorrect
150 = 2 (l + 20). Hence, l + 20 = 150 ÷ 2 = 75, or l = 75 - 20 = 55 cm.

### 2The length and width of a rectangle are 35 cm and 25 cm, respectively. What is the perimeter of this rectangle?

100 cm
110 cm
115 cm
120 cm
CorrectIncorrect
P = 2(35+25) = 2(60) = 120 cm

### 3The length of a rectangle is twice its width. If the width of a rectangle is 45 cm, calculate the perimeter of the rectangle.

135 cm
170 cm
200 cm
270 cm
CorrectIncorrect
Length = 2(width) = 2(45) = 90 cm. So, P = 2(90 + 45) = 2(135) = 270 cm.

### 4The perimeter of a rectangle is 250 cm. The length of the rectangle is 1/5th of the perimeter. What is the width of the rectangle?

60 cm
75 cm
100 cm
150 cm
CorrectIncorrect
Length = ⅕ (250) = 50 cm. Now, P = 2 (50 + w) = 250. So, w = $\frac{250}{2}$ – 50 = 75 cm
Perimeter of Rectangle = 2 (Length + Width). Rearranging the terms in this formula, we get, Length = $\frac{Perimeter}{2}$ – Width. So, to find the length of a rectangle, subtract the width from half of the perimeter.