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
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)
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.
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.
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.
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.
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.
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?
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
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.
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.
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