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
From Perimeter of a Rectangle to HOME PAGE
Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.
Feb 24, 24 04:33 PM
Feb 24, 24 04:11 PM
Feb 24, 24 04:10 PM
Feb 24, 24 04:09 PM
Feb 24, 24 10:59 AM
New! Comments
Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.