If the areas of two circles are in the ratio 4:9, then the ratio of their perimeters of their semi-circles is:

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Solution

Q.
If the areas of two circles are in the ratio 4:9, then the ratio of their perimeters of their semi-circles is:

1 2:3

2 $3 : 2$

3 $1 : 2$

4 $1 : 3$

Ans.
(1)

Let the radii of two circles be $r_{1} a n d r_{2}$ . It is given that

$π r_{1}^{2} : π r_{2}^{2} = 4 : 9 \Rightarrow r_{1}^{2} : r_{2}^{2} = 4 : 9 \Rightarrow r_{1} : r_{2} = 2 : 3 L e t P_{1} a n d P_{2} b e t h e p e r i m e t e r s o f t h e t w o s e m i - c i r c l e s . T h e n, P_{1} = π r_{1} + 2 r_{1} P_{2} = π r_{2} + 2 r_{2} \Rightarrow P_{1} = (π + 2) r_{1} and P_{2} = (π + 2) r_{2} \Rightarrow P_{1} : P_{2} = r_{1} : r_{2} = 2 : 3$

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