If the ratio of areas of circles are $4 : 9 : 25$ what is the ratio of their radii.

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Solution

Step 1: Find the relation between the areas of circles.
Assume that, $r_{1}, r_{2}, r_{3}$ be the radii of the circles.
According to the given information, ratio of area i.e.
$π {(r_{1})}^{2} : π {(r_{2})}^{2} : π {(r_{3})}^{2} = 4 : 9 : 25$
Step 2: Find the required ratio of radii
Since, It is given that $π {(r_{1})}^{2} : π {(r_{2})}^{2} : π {(r_{3})}^{2} = 4 : 9 : 25$ .
Therefore, ${(r_{1})}^{2} : {(r_{2})}^{2} : {(r_{3})}^{2} = 4 : 9 : 25$ .
Take square root on both sides.
$\Rightarrow r_{1} : r_{2} : r_{3} = 2 : 3 : 5$
Hence, the ratio of the radii of the circles are $2 : 3 : 5$ .

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Similar questions

The radii of two circles are in the ratio $2 : 3$ . The ratio of their areas is
$(a)$ $2 : 3$

$(b)$ $4 : 9$

$(c)$ $3 : 2$

$(d)$ $9 : 4$

4 : 9

3 : 4

4 : 9

4 : 9

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