# Perimeter of a Rectangle

We will discuss here how to find the perimeter of a rectangle. We know perimeter of a rectangle is the total length (distance) of the boundary of a rectangle.

In a rectangle we know that two opposite sides are equal. So, PQ = SR and PS = QR

If PS = l and PQ = b

Perimeter of the rectangle = PQ + QR + RS + SP

= b +l + b + l

= 2b +2l

Again,

ABCD is a rectangle. We know that the opposite sides of a rectangle are equal.

AB = CD = 5 cm and BC = AD = 3 cm

So, the perimeter of the rectangle ABCD = AB + BC + CD + AD = 5 cm + 3 cm + 5 cm + 3 cm = 16 cm

It can be written as 5 cm + 5 cm + 3 cm + 3 cm

= (2 × 5) cm + (2 × 3) cm

= 2 (5 + 3) cm

= 2 × 8 cm

= 16 cm

We add length and breadth twice to find the perimeter of a rectangle.

Perimeter of a rectangle = 2 (length + breadth)

A rectangle is a four sided figure in which

● Opposite sides are equal in length.

● Longer side is called length and shorter side is called breadth.

● All angles are equal to 90° (right angle).

In the above figure ABCD is a rectangle.

Three children found the perimeter of this rectangle in three different methods.

1st method:

Perimeter = 6 cm + 4 cm + 6 cm + 4 cm                                = 20 cm

2nd method:

Perimeter = (2 6 cm) + (2  4 cm)              = 12 cm + 8 cm     =  20 cm

3rd method:

Perimeter = 2 (6 cm + 4 cm)                    = 2 cm × 10 cm      = 20 cm

All the three methods gave them the same answer.

Perimeter of a rectangle = length + breadth + length + breadth

= (2 length) + (2 breadth)

Word Problems on Perimeter of a Rectangle:

Let us consider some of the examples on perimeter of a rectangle:

1. The length of a rectangle is 4 cm and its breadth is 2 cm. Find its perimeter.

Solution:

Length = 4 cm

Therefore, perimeter of the rectangle

= 2 (4 + 2) cm

= 2 × 6 cm

= 12 cm

2. Find the perimeter of the rectangle ABCD whose sides are 6 cm and 5 cm.

Solution:

The perimeter of the rectangle ABCD

= 6 cm + 5 cm + 6 cm + 5cm

= 22 cm

3. Find the perimeter of a rectangle whose length is 12 cm and breadth is 8 cm.

Solution:

Length = 12 cm

Perimeter = 2 (length + breadth)

= 2 (12 cm + 8 cm)

= 2 × 20 cm

= 40 cm

4. A rectangular swimming pool is 9 m long and 4 m broad. Find the area of the swimming pool.

Solution:

Length of the rectangular swimming pool = 9 m

Breadth of the rectangular swimming pool = 4 m

Therefore, perimeter of the rectangle swimming pool

= 2 (9 + 4) m

= 2 (13) m

= 2 × 13 m

= 26 m

5. The length of a rectangle is 4.5 m and the breadth is 1.5 m. Find the perimeter.

Solution:

Length = 4.5 m

Perimeter = 2 (length + breadth)

= 2 × (4.5 m + 1.5 m)

= 2 × 6 m

= 12 m

Therefore, the perimeter is 12 m.

6. How to find the perimeter of a rectangle?

Find the perimeter of the given figure.

Solution:

A rectangle has four sides.

To find the perimeter of a rectangle, we measure all the four sides of the figure and add them together.

In the above given figure, length of the 4 sides are = 6 cm, 3 cm, 6 cm, 3 cm.

Therefore, perimeter of the square = 6 cm + 3 cm + 6 cm + 3 cm

= 18 cm

7. A rectangle display board is measuring 8 m by 6 m. Robert wants to add a ribbon border around the display board. What is the length of ribbon that he will need? If the cost of the ribbon is $15 per metre then how much money does Robert needs to buy the ribbon? Solution: Length of the display board = 8 m Breadth of the display board = 6 m Perimeter of the display board = 2 (Length + Breadth) = 2 (8 + 6) m = 2 × 14 m = 28 m. Cost of ribbon is$15 per meter.

Therefore, total cost for 28 m long ribbon = $15 × 28 =$420.

Worksheet on Perimeter of a Rectangle:

1. Find the perimeter of the rectangles having measurements as follows.

(i) length = 11 cm breadth = 9 cm

(ii) length = 5 cm breadth = 2 cm

(iii) length = 10 cm breadth = 8 cm

(iv) length = 15 cm breadth = 2 cm

1. (i) 40 cm

(ii) 14 cm

(iii) 36 cm

(iv) 34 cm

Perimeter of a Rectangle Word Problems

2. A rectangle has a perimeter of 40 cm. If its length is 8 cm, what is its breath?

2. 12 cm

3. Sam is running around a rectangular park of length 450 m and breadth 300 m. Find the total distance covered by him if he takes 10 rounds of the park.

3. 15000 m

4. A gardener wants to fence its rectangular garden with a wire. The length and breadth of the garden is 25 m and 16 m respectively. Find the length of the wire he must buy.

4. 82 m

5. Find the perimeter of each of the following rectangles using formula:

5. (i) Perimeter of the rectangle 16 cm.

(ii) Perimeter of the rectangle 28 cm.

(iii) Perimeter of the rectangle 26 cm.

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