The area of the greatest circle which can be inscribed in a square whose perimeter is 120 cm, is :

A. $$\frac{{22}}{7} \times {\left( {\frac{7}{2}} \right)^2}c{m^2}$$

B. $$\frac{{22}}{7} \times {\left( {\frac{9}{2}} \right)^2}c{m^2}$$

C. $$\frac{{22}}{7} \times {\left( {\frac{15}{2}} \right)^2}c{m^2}$$

D. $$\frac{{22}}{7} \times {\left( {15} \right)^2}c{m^2}$$

Answer: Option D

Solution(By Examveda Team)

Side of the square :
$$\eqalign{ & = \frac{{120}}{4}cm \cr & = 30\,cm \cr} $$
Radius of the required circle :
$$\eqalign{ & = \left( {\frac{1}{2} \times 30} \right)cm \cr & = 15\,cm \cr & = \pi \times {r^2} \cr & = \left[ {\frac{{22}}{7} \times {{\left( {15} \right)}^2}} \right]c{m^2} \cr} $$