Question

What will be the side of the square whose area is equal to the area of rectangle with length and breadth equal to $20\text{cm}$ and $24\text{cm}$ respectively?

• A. $20\text{cm}$
• B. $2\sqrt{30}\text{cm}$
• C. $24\text{cm}$
• D. $4\sqrt{30}\text{cm}$

Answer 1

The correct option is D $4\sqrt{30}\text{cm}$

We know that the area of rectangle is calculated as

$A=l\times b$,

where $A$ is the area of rectangle, $l$ is the length and $b$ is the breadth of the rectangle.



Given: $l=20\text{cm}$ and $b=24\text{cm}$

$\begin{array}{cc}\therefore A& =20\times 24\\ & =480\end{array}$

Hence, the area of rectangle is $480{\text{cm}}^2$.

It is also given that the area of square is equal to the area of rectangle.

$\therefore \text{Area of square}=480{\text{cm}}^2$.

The formula to calculate the area of square is given as,

$\text{Area of square}=a^2$,

where $a$ is the side of the square.



Substitute the value of area of square in the formula to calculate its side.

$\begin{array}{cc}480& =a^2\\ a& =\pm \sqrt{480}\\ & =\pm 4\sqrt{30}\end{array}$

Since side cannot be negative, therefore $a=4\sqrt{30}$.

Thus, the side of the given square is $4\sqrt{30}\text{cm}$.