the diameter of 2 circles are in the ratio of 5 :12 and the sum of their areas is equal to the area of a circle of radius 13 cm . find the diameters of the given circles .

If the diameters are in the ratio 5:12, same is the radii,
let the multiple be: x
then radii of both the circles are 5x and 12x
pi(5x)² + pi(12)² = pi(13)²
dviding by pi,
25x² + 144x²=169
169x²=169
x²=1
x=1cm
So, the radii are: 5cm and 12cm, while the diameters are 10cm and 24 cm