Question

The area of a Rectangle and a square are the same. If the length and breadth of the rectangle are $27cm$ and $3cm$ respectively, then find the side of the square.

Answer 1

Hint: Given, Area of square is equal to area of the rectangle. First, We need to find the area of the rectangle using the given value of length and breadth. From this, we need to find the value of the sides of the square.

Formula used:

1. Area of a Rectangle= Length $\times$ Breadth  

2. Area of a Square=  $ {(side)^2} $.

Complete step-by-step answer:

Let us consider a rectangle ABCD of Length (L) and breadth (B)

So, Area of rectangle ABCD= Length (L) $\times $Breadth (B)

But, as per the question, Length (L) is given as 27cm and Breadth (B) is given as 3cm.

Hence, Area of rectangle ABCD  $ 27\times 3 $

So, Area of rectangle ABCD  $  = 81c{m^2} $ 

Now, let us consider a square EFGH of side (a)

Since, all the four sides of a square are equal, we can consider the area of the square as the product of side x side

So, Area of a square=  $ {(side)^2} $ , Let the side of the square be $a$.

Hence, Area of the square EFGH=$ a \times a =  {a^2} $ 

According to the question,

Give, Area of the rectangle = Area of the square</b>

i.e. Length $\times$ breadth =  $ {(side)^2} $ 

 $ \Rightarrow $ ,  $ 81c{m^2} = {a^2} $ 

So, the side of the square EFGH (a)=  $ \sqrt {81c{m^2}}  $ 

$= 9cm.$

Therefore, The side of the given square will be 9cm.

Note: To solve the above problem we just need to remember the formulas of area of rectangle and square. Besides, the rectangle and square are both quadrilaterals having all the interior angles as right angles. And every square is a rectangle but every square is not a rectangle, because a rectangle can be considered to be a square only when its length is equal to its breadth.