Question

The area of a square is $576c{m}^2$. Find the length of its side and diagonal.

• A. $24cm,32.84cm$
• B. $25cm,33.84cm$
• C. $24cm,33.94cm$
• D. $24cm,33.54cm$

Answer 1

Answer: (C)

Given:

Area of square $=576c{m}^2$

Let length of the side of the square be $a$.

We know that, Area of the square $=a^2$ sq. units

$\Rightarrow a^2=576c{m}^2$

$\Rightarrow a=\sqrt{576c{m}^2}$

$\Rightarrow a=24cm$

Therefore, the side of the square is $24cm$

We know that, if side of the square is $a$ then length of its diagonal is $\sqrt{2}a$

$\Rightarrow$ Length of the diagonal $=\sqrt{2}\times 24cm=24\sqrt{2}cm$

We know that, $\sqrt{2}=1.414$ (approximately)

$\Rightarrow$ Length of the diagonal $=24\times 1.414cm=33.936cm$

$\Rightarrow$ Length of the diagonal $=33.94cm$ (approximately)

Hence, Option $C$ is correct.