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