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 a Rectangle

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.

Perimeter of a Rectangle

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)


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

Examples on Perimeter of a Rectangle

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:

Perimeter of Rectangle

The perimeter of the rectangle ABCD

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

= 22 cm


3. 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


4. 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 of a Rectangle Problems

Perimeter = 2 (length + breadth)

               = 2 × (4.5 m + 1.5 m)

               = 2 × 6 m

               = 12 m

Therefore, the perimeter is 12 m.


5. 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. 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:

15000 m


2. 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:

82 m

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