Find the length of the diagonal of a square whose area is 128 cm2.

Solution:

Area of the square = 128 cm2

Area $=\frac{1}{2} d^{2} \quad$ (where $d$ is a diagonal of the square)

$\Rightarrow 128=\frac{1}{2} d^{2}$

$\Rightarrow d^{2}=256$

$\Rightarrow d=16 \mathrm{~cm}$

Now,

Area = Side $^{2}$

$\Rightarrow 128=$ Side $^{2}$

 

$\Rightarrow$ Side $=11.31 \mathrm{~cm}$

Perimeter = 4(Side)

$=4(11.31)$

 

$=45.24 \mathrm{~cm}$

Thus, the perimeter of the square is 45.24 cm.