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)


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).

Perimeter of a Rectangle

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

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. 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 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.


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

Units for Measuring Length

Measuring Instruments

To Measure the Length of a Line-segment

Perimeter of a Figure

Perimeter of a Triangle

Perimeter of a Rectangle

Perimeter of a Square

Unit of Mass or Weight

Examples on Unit of Mass or Weight

Units for The Measurement of Capacity

Examples on Measurement of Capacity

Measurement of Time

Read a Watch or a Clock

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

What Time it is?

Time in Hours and Minutes

24 Hour Clock

Units of Time

Examples Units of Time

Time Duration

Calendar

Reading and Interpreting a Calendar

Calendar Guides us to Know



4th Grade Math Activities

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