Question

The diameters of two given circles are in the ratio 12 : 5 and the sum for their areas is equal to the area of a circle of diameter 65 cm. what are their radius ?

Answer 1

area of circle having radius 65/2 cm=πr²=22/7(65/2)²=π×65×65/4
now if the ratio of diameters of two circles is 12:5
the ratio of their radius also12:5
let their radius are 12x,5x
sum of their areas=
22/7(12x+5x)²
=π×17×17x²=π×65×65/2×2
=x²=65²/(17²×4)
x=√65²/√17²√2²=65/(17×2)=65/34
12x=12×65/34=6×65/17=390/17cm
5x=5×65/34=325/34cm