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

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

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

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

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

Solution:

Side of the square :

\begin{aligned} = \frac{120}{4} c m \\ = 30 c m \end{aligned}

Radius of the required circle :

\begin{aligned} = (\frac{1}{2} \times 30) c m \\ = 15 c m \\ = π \times r^{2} \\ = [\frac{22}{7} \times {(15)}^{2}] c m^{2} \end{aligned}

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