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.

**1 ^{st} method:**

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

**2 ^{nd} method:**

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

**3 ^{rd} 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)*

* =
2 (length + 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

Breadth = 2 cm

Therefore, perimeter of the rectangle

= 2 (length + breadth)

= 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

Breadth = 8 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 (length + breadth)

= 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

Breadth = 1.5 m

Perimeter = 2 (length + breadth)

= 2 × (4.5 m + 1.5 m)

= 2 × 6 m

= 12 m

Therefore, the perimeter is 12 m.

**6.** 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 metre.

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

= $420.

Questions and Answers 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

**Answer:**

**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?

**Answer:**

**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.

**Answer:**

**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.

**Answer:**

**4.** 82 m

**● ****Related Concepts**

**● ****To
Measure the Length of a Line-segment**** **

**● ****Examples
on Unit of Mass or Weight**

**● ****Units
for The Measurement of Capacity**

**● ****Examples
on Measurement of Capacity**

**● ****Antemeridian
(a.m.) or Postmeridian (p.m.)**

**● ****Calendar**

**● ****Reading
and Interpreting a Calendar**

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