Question

The perimeter of a square and a rectangle are equal. If the length and breadth of the rectangle are 12cm and 10cm respectively, find the area of the square.

Answer 1

Step-by-step explanation:

perimeter of square=perimeter of rectangle

4a=2(l+b)

4a=2(12+10)cm

4a=44cm

a=11cm

side of square =11cm

area=a^2

area = 11^2

area= 121cm^2

Answer 2

Given :-

Perimeter of a square is equal to the perimeter of a rectangle

Length of the rectangle = 12 cm

Breadth of the rectangle = 10 cm

Required to find :-

• Area of the square

Formulae used :-

$\large{\leadsto{\boxed{\rm{Area\;of\;a\;rectangle=length \times breadth}}}}$

$\large{\leadsto{\boxed{\rm{Area\;of\;a\;square=side \times side}}}}$

$\large{\leadsto{\boxed{\rm{Perimeter\;of\;the\;rectangle= 2 ( length + breadth )}}}}$

$\large{\leadsto{\boxed{\rm{perimeter \;of\;a\;square=4 \times side }}}}$

Solution :-

Given that :-

Perimeter of the square is equal to perimeter of a rectangle

Length = 12 cm

Breadth = 10 cm

He asked us to find the area of a square .

So,

Let's consider the measurements of the rectangle .

Length of the rectangle = 12 cm

Breadth of the rectangle = 10 cm

Using the formula ,

$\large{\leadsto{\boxed{\rm{Perimeter\;of\;the\;rectangle= 2 ( length + breadth )}}}}$

substitute the required values

So,

$\longrightarrow{\tt{perimeter = 2 ( 12 + 10 ) }}$

$\longrightarrow{\tt{perimeter = 2 ( 22 ) }}$

$\longrightarrow{\tt{ Perimeter = 44 cm }}$

Hence

Perimeter of a rectangle is 44 cm

It is given that ,

Perimeter of a rectangle = Perimeter of a square

So,

Perimeter of a square = 44 cm

Now we have to find the measurement of the length of side of a square .

So,

Let the side be " x " cm .

using the formula

$\large{\leadsto{\boxed{\rm{Perimeter\;of\;a\;square=side \times 4}}}}$

$\longrightarrow{\rm{ 44 = x \times 4 }}$

$\longrightarrow{\rm{ 44 = 4x }}$

Interchange the terms on both sides

$\longrightarrow{\tt{ 4x = 44 }}$

$\longrightarrow{\tt{ x = \dfrac{44}{4}}}$

$\longrightarrow{\tt{ x = 11 }}$

Hence,

Side of a square is 11 cm .

Using the formula

$\large{\leadsto{\boxed{\rm{Area\;of\;a\;square=side \times side}}}}$

So,

$\longrightarrow{\rm{Area = 11 \times 11 }}$

$\longrightarrow{\rm{Area = 121 {cm}^{2} }}$

$\large{\leadsto{\boxed{\rm{\therefore{Area\;of\;a\;square = 121 {cm}^{2} }}}}}$