The area of two circles are in the ratio 49 is to 64 find the ratio of their circumference

Given, the area of two circles are in the ratio 49:64

Area of a circle = `pir^2`

Let area of the first circle = `pir_1^2`

And area of the second circle = `pir_2^2`

`49/64 = r_1^2/r_2^2`

⇒ `49/64 = r_1^2/r_2^2`

⇒ `(7)^2/(8)^2 = r_1^2/r_2^2`

⇒ `(7/8)^2 = (r_1/r_2)^2`

∴ r1 = 7 and r2 = 8

The ratio of circumferences of these two circles = `(2pir_1)/(2pir_2) = r_1/r_2 = 7/8`   ......[∵ Circumference of circle = 2πr]

Hence, required ratio is 7:8