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

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Solution

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

1 $22 : 7$

2 $14 : 11$

3 $7 : 22$

4 $11 : 14$

Ans.
(2)

Let r be the radius of the circle and x be the length of each side of the square.

According to the question, Perimeter of circle = Perimeter of square

$2 π r = 4 x \Rightarrow π r = 2 x \Rightarrow r = \frac{2 x}{π} (i) \Rightarrow \frac{Area of circle}{Area of square} = \frac{π r^{2}}{x^{2}} = \frac{π \times \frac{4 x^{2}}{π^{2}}}{x^{2}} = \frac{4}{π} \Rightarrow \frac{Area of circle}{Area of square} = \frac{4}{\frac{22}{7}} = \frac{4}{\frac{22}{7}} \times 7 = \frac{28}{22} = \frac{14}{11} R e q u i r e d r a t i o i s 14 : 11$

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