If the perimeter of a circle is equal


If the perimeter of a circle is equal to that of a square, then the ratio of their areas is

(a) 22 :7                    

(b) 14:11                  

(c) 7:22                     

(d) 11:14


(b) Let radius of circle be r and side of a square be a.

According to the given condition,

Perimeter of a circle $=$ Perimeter of a square

$\because$ $2 \pi r=4 a \Rightarrow a=\frac{\pi r}{2}$ $\ldots$ (i)

 Now, $\frac{\text { Area of circle }}{\text { Area of square }}=\frac{\pi r^{2}}{(a)^{2}}=\frac{\pi r^{2}}{\left(\frac{\pi r}{2}\right)^{2}}$ [from Eq. (i)]

$=\frac{\pi r^{2}}{\pi^{2} r^{2} / 4}=\frac{4}{\pi}=\frac{4}{22 / 7}=\frac{28}{22}=\frac{14}{11}$

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