Question

The length and breadth of rectangle are 12 cm and 9 cm respectively. Find the side of the square with
perimeter equal to that of the rectangle?
​

Answer 1

Answer:

Given : Length and breadth of the rectangle are 12 cm and 9cm respectively.

To find: The side of a square with its perimeter equal to that of the rectangle.

Answer :-

First, let's find the perimeter of the rectangle.

Formula :-

Perimeter = 2(l + b )

Substituting the respective values,

Perimeter = 2 x ( l + b )

= 2 x ( 12 + 9 )

= 2 x 21

= 42

Perimeter = 42 cm

Now, perimeter of rectangle = perimeter of sqaure.

So, Formula (to find perimeter of a square): 4S = Perimeter.

Substituting the value of the perimeter,

4S = 42cm

S = 42/44

S = 10.5cm

Proof :-

Perimeter of sqaure = 4 x side

Substituting the value of side,

4 x 10.5 = 42 cm

Answer 2

Given :

The length and breadth of rectangle are 12 cm and 9 cm respectively. The perimeter of rectangle is equal to the perimeter of the square.

To Find :

The side of square.

Solution :

Analysis :

Here we first have to find the perimeter of the rectangle. As it is given that the perimeter of rectangle is equal to the perimeter of square therefore we can use that information and find the side of square.

Required Formula :

• Perimeter of Rectangle = 2(l + b)

• Perimeter of square = 4 × side

where,

• l = Length
• b = Breadth

Explanation :

We know that if we are given the length and breadth of the rectangle and is asked to find the perimeter of rectangle then our required formula is,

Perimeter of Rectangle = 2(l + b)

where,

• l = 12 cm
• b = 9 cm

Using the required formula and substituting the required values,

⇒ Perimeter of Rectangle = 2(l + b)

⇒ Perimeter of Rectangle = 2(12 + 9)

⇒ Perimeter of Rectangle = 2(21)

⇒ Perimeter of Rectangle = 2 × 21

⇒ Perimeter of Rectangle = 42

∴ Perimeter of Rectangle = 42 cm.

• It is said that the perimeter of rectangle is equal to perimeter of square.

☯ According to the question,

⇒ Perimeter₍ᵣₑ꜀ₜₐₙ₉ₗₑ₎ = Perimeter₍ₛqᵤₐᵣₑ₎

⇒ 42 cm = 42 cm

∴ Perimeter of Square = 42 cm.

Let us assume that the side of the square is "x" cm.

We know that if we are given the perimeter of square and is asked to find the side of square then our required formula is,

Perimeter of square = 4 × side

where,

• Perimeter = 42 cm
• Side = s cm

Using the required formula and substituting the required values,

⇒ Perimeter of square = 4 × side

⇒ 42 = 4 × s

⇒ 42/4 = s

⇒ 10.5 = s

∴ Side = 10.5 cm.

The side of thr square is 10.5 cm.

Verification :

⇒ Perimeter of square = 4 × side

Putting side = 10.5,

⇒ 42 = 4 × 10.5

⇒ 42 = 42

∴ LHS = RHS.

• Hence verified .