The areas of two circles are in the ratio 49 : 36. The ratio of their circumferences is

(a) 7 : 6 (b) 6 : 7 (c) 3 : 2 (d) 2 : 3

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Solution

Let r₁ and r₂ be the radius of the two circles. Then
$\frac{π {r_{1}}^{2}}{π {r_{2}}^{2}} = \frac{49}{36} \Rightarrow {(\frac{r_{1}}{r_{2}})}^{2} = {(\frac{7}{6})}^{2} \Rightarrow \frac{r_{1}}{r_{2}} = \frac{7}{6}$
Now
$Ratio of circumferences = \frac{2 π r_{1}}{2 π r_{2}} = \frac{r_{1}}{r_{2}} = \frac{7}{6}$
Thus, the required ratio is 7 : 6.
Hence, the correct option is (a).

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