## Perimeter of a Rectangle

Rectangles are four-sided polygons. Following are the properties of a rectangle:

- (i) All the angles of a rectangle are 90º.
- (ii) Opposite sides of a rectangle are always the same in size.

## Perimeter of a rectangle

The perimeter of a rectangle is the total length of all the sides of the rectangle. Hence, we can find the perimeter by adding all four sides of a rectangle.

Perimeter of the given rectangle is a + b + a + b. Since opposite sides of a rectangle are always equal, we need to find the dimensions of only two sides to find the perimeter of a rectangle.

The perimeter of the above rectangle with sides ‘a units’ and ‘b units’ is:

a + b + a + b = 2a + 2b = 2 (a + b) units.

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

**Examples of finding the perimeter of a rectangle**
**Example 1.** The two sides of the rectangle are given. What will be the perimeter of the rectangle?

**Solution:** One side of the rectangle is 2 cm and the other side is 5 cm.

We know that, the perimeter of a rectangle = 2 × (sum of adjacent sides)

Therefore, the perimeter of the rectangle = 2 × (5 + 2) = 2 × (7) = 14 cm

**Example 2.** A rectangular playground is 20 m long and 13 m wide. Find its perimeter.

**Solution:** One side of the rectangular playground is 20 m and the other side is 13 m.

We know that, the perimeter of a rectangle = 2 × (sum of adjacent sides)

Therefore, the perimeter of the rectangular ground = 2 × (20 + 13) = 2 × (33) = 66 m

## Tricky problems involving perimeter of rectangles

**Type I:** When the perimeter and only one of the sides are given.

**Example 1.** If the perimeter of the given rectangle is 10 cm and the length of one of its sides is 2 cm. What will be the other side?

**Solution:** The perimeter of the rectangle, with one of the sides equal to 2 cm, is 10 cm.

Let the missing side be ‘a’.

We know that, the perimeter of a rectangle = 2 × (sum of adjacent sides)

10 = 2 × (2 + a) 5 = (2 + a)

a = 5 - 2 = 3 cm

**Type II:** Finding sides using the properties of a rectangle.

**Example 2.** In the given rectangle, if a = 4 cm and d = 3 cm. Find b and c.

**Solution:** We know that side a = 4 cm and side d = 3 cm.

To find side b and c, we use the property that the opposite sides of a rectangle are always the same in size.

Hence, a = c = 4 cm and d = b = 3 cm.