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