Question

if the ratio of areas of two circles is 4:9, then the ratio of their circumference will be

Answer 1

2:3 is the correct answer 

Answer 2

Radius of first circle = R1

Radius of second circle = R2

$\frac{area \: of \:first \: circle }{area \: of \: second \: circle} = \frac{4}{9} \\ \frac{\pi \:R {1}^{2} }{\pi \:R2² } = \frac{4}{9} \\ \frac{R1²}{R2²} = \frac{2²}{3²} \\ \frac{R1}{R2} = \frac{2}{3}$

$\frac{circumference \: of \: first \: circle }{circumference \: of \: second \: circle } = \frac{2\pi \: R1}{2\pi \: R2} \\ \\ \frac{circumference \: of \: first \: circle }{circumference \: of \: second \: circle } = \frac{r1}{r2} \\ \\ \frac{circumference \: of \: first \: circle }{circumference \: of \: second \: circle } = \frac{2}{3}$