This article features a collection of questions and answers on the perimeter of a rectangle to assist students in mastering this topic. The perimeter of a shape refers to its outer boundary. To accelerate your understanding, we have compiled a list of questions related to the perimeter of a rectangle, complete with detailed solutions. To learn more about the concept of a rectangle's perimeter, click here .

Perimeter of a Rectangle

The perimeter of a rectangle means the total distance around the outside of the rectangle. It is the length of all four sides added together.

We usually measure this in units like meters, inches, feet, or yards, because it's a straight-line distance.

Maths Notes Free PDFs

Basic Properties of a Rectangle:

1. A rectangle has four corners, and each corner is a right angle (90 degrees).
2. The opposite sides of a rectangle are always equal in length.

Formula for Perimeter of Rectangle

The perimeter of a rectangle is the total distance around it. To find it, we add the length and the breadth (width) of the rectangle, and then multiply the result by 2.

Formula:
Perimeter = 2 × (Length + Breadth)

1. What is the perimeter of a rectangle with a length of 15 cm and a breadth of 10 cm?

Solution:

We can find the perimeter of the rectangle using its formula.

As we know,

Perimeter of rectangle = 2(length + breadth) units.

Given that, Length = 15 cm, and breadth = 10 cm.

Substituting the values in the perimeter formula, we get

Perimeter of rectangle = 2(15 + 10)

Perimeter = 2(25)

Perimeter = 50 cm.

Therefore, the perimeter of the rectangle is 50 cm.

2. A tablecloth has a length of 150 inches and a breadth of 120 inches. How much lace will be required to complete the border?

Solution:

To find out the amount of lace required for the border of the tablecloth, we need to calculate the perimeter of the tablecloth using the rectangle's perimeter formula.

Given,

Length, l = 150 inches

Breadth, b = 120 inches.

As we know, the perimeter of a rectangle = 2(l + b) units.

Substituting the values in the formula, we get

Perimeter = 2(150 + 120) = 2 × 270 = 540 inches.

Hence, we will need 540 inches of lace to complete the border.

3. Find the perimeter of a rectangle where its length is 7 cm, and breadth is 5 cm.

Solution:

Given that, Length, l = 7 cm

Breadth, b = 5 cm

The formula to calculate the perimeter of a rectangle is given as follows:

Perimeter = 2 × (Length + Breadth) units.

Substituting the values in the formula, we get

Perimeter = 2 × (7 + 5) cm

Perimeter = 2 (12) cm

Perimeter = 24 cm

Hence, the perimeter of the rectangle is 24 cm.

4. The length of a rectangular field is 100 m, and its perimeter is 300 m. Find the breadth of the rectangular field.

Solution:

Given: Perimeter = 300 m and length, l = 100 m.

To find: Breadth (b).

As we know, rectangle’s perimeter = 2 (l + b)

Substituting the given values, we derive the following:

2(l + b) = 300 m

Dividing both sides by 2, we get

l + b = 150 m

Substituting l = 100 m, we get

100 + b = 150 m

Simplifying the above equation, we get

b = 150 – 100 m

b = 50 m

Hence, the breadth of the rectangular field is 50 m.

5. Determine the breadth of a rectangular plot if its area is 500 m 2 and the length is 25 m. Also, find its perimeter.

Solution:

Given: Area of rectangular plot = 500 m 2 .

Length = 25 m.

To find : Breadth and perimeter of the rectangular plot.

As we know, Area = Length × Breadth

Substituting the given values in the formula to find the breadth, we get

500 = 25 × Breadth

Breadth = 500/25 = 20 m

Therefore, the breadth of the rectangular plot = 20 m.

Substituting the length and breadth values in the perimeter formula, we get

Perimeter = 2 (Length + Breadth) units

Perimeter = 2 (25 + 20)

Perimeter = 2 (45)

Perimeter = 90 m

Therefore, the perimeter of the rectangular plot of land is 90 m.

Further reading: Rectangle .

6. Find the perimeter of a rectangle as shown in the figure below:

Solution:

From the given figure, it is observed that,

Length = 35 cm and breadth = 25 cm.

Substituting these values in the perimeter of rectangle formula, we get

Perimeter of rectangle = 2 × (length + breadth) units

Perimeter = 2 × (35 + 25)

Perimeter = 2 × 60

Perimeter = 120 cm

Therefore, the perimeter of the rectangle, if length = 35 cm and breadth = 25 cm, is 120 cm.

7. A rectangle has a perimeter of 60 meters. Its length is 6 meters shorter than four times its breadth. What is the area of the rectangle?

Solution:

Given: Perimeter of rectangle = 60 m.

Let's assume the rectangle’s breadth is y.

According to the given condition, the rectangle’s length will be 4y−6.

As we know, perimeter of rectangle = 2(length + breadth) units

Substituting the obtained values in the formula, we get

⇒ 60 = 2(4y−6+y)

Simplifying the above equation, we get

⇒ 60 = 2 (5y- 6)

⇒ 60 = 10y- 12

⇒ 10y = 60+12

⇒ 10y = 72

⇒ y = 72/10

⇒ y = 7.2

Therefore, the breadth of the rectangle = 7.2 m.

So, Length = 4(7.2) – 6

Length = 28.8 – 6

Length = 22.8

Hence, the length of the rectangle = 22.8 m.

We know that,

Area of rectangle = length × breadth square units.

Area = 22.8 × 7.2 m 2

Area = 164.16 m 2

Hence, the area of the rectangle is 164.16 m 2 .

8. As shown in the figure below, rectangle ABCD is made up of 4 equal rectangles. Find the perimeter of ABCD if one of the rectangles has an area of 12 m 2 and a breadth of 3 m.

Solution:

Let's denote the given figure as follows:

Given that, the area of one rectangle is 12m 2

Also, breadth = 3m

As we know, Area = length × breadth

Substituting the given values in the formula, we get

⇒ length × breadth = 12

⇒ length × 3 = 12

⇒ length = 4 m

Since all the four rectangles are equal, all the rectangles have a length 4 m and a breadth 3m.

The perimeter of rectangle ABCD is given by:

= AB + BC + CD + DA + AE + EF + FA

Here, small lengths represent the breadth, while longer lengths represent the length.

Therefore, perimeter of rectangle ABCD = 4 + 3 + 4 + 3 + 4 + 3 + 4 + 3 = 28m

Thus, the perimeter of the rectangle ABCD is 28 metres.

9. A rectangle with a perimeter of 396 cm is divided into 6 equal rectangles, as shown in the figure below. What is the perimeter of one of the rectangles?

Solution:

Given that rectangle’s perimeter = 396 cm.

Also, The rectangle is divided into 6 equal rectangles.

To find: Perimeter of one rectangle.

Let's denote the figure as shown below with the letters “l” and “b”.

Assume that, length = l and breadth = b

As we know, rectangle’s perimeter = 2(length + breadth) units

From the diagram as shown above, the perimeter of a rectangle is calculated as follows:

= l + b + l + l + b + l + b + b + b

= 4l + 5b

Therefore, 396 = 4l + 5b … (1)

In addition, the figure shows that the 3 breadth of the top vertical rectangles is equal to the 2 lengths of the 2 bottom horizontal rectangles.

Hence, we can write,

2l = 3b … (2)

Substituting (2) in (1), we get

396 = 2(3b) + 5b

Simplifying the above equation, we get

396 = 6b + 5b

11b = 396

b = 396/11

b = 36 cm

Hence, breadth = 36 m

Substituting b = 36 in (2), we get

2l = 3(36)

l = 3(36)/2

l = 3(18)

l = 54 cm

Hence, length = 54 cm

Therefore, the perimeter of one rectangle = 2(54 + 36)

= 2(90)

= 180 cm

Therefore, one of the rectangles’ perimeter is 180 cm.

10. For her toy car, Ria created a miniature round race track. The illustration below shows her concept. What is the total distance around the track? Round your answer to the nearest whole centimetre.

Solution:

The perimeter of the given track = Total distance around the track

The track consists of two semi-circular paths and a rectangular path.

Therefore, the perimeter of the given track = 62 + 62 + 2πr

Perimeter = 62 + 62 + [2(22/7)20]

Perimeter = 124+125.71

Perimeter = 249.71 ≈ 250 cm.

Hence, the total distance around the track rounded to the nearest whole centimetre is 250 cm.

Practice Questions

• Find the length and perimeter of a rectangle whose area is 108 cm 2 and breadth is 9 cm.
• Calculate the perimeter of a rectangle, given that the area of a rectangle is 280 sq. cm and the length is 28 cm.
• Determine the perimeter of a rectangle whose length, l = 8 cm and b = 6 cm.

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