The radii of two circles are 20 cm and 15 cm respectively. If a third circle has an area which is equal to the sum of the areas of the two given circles, what will be the radius of the third circle?
Let the radius of three circles be $$r_1, r_2,r_3 cm$$
Given, $$r_1 = 20 cm$$
$$r_2 = 15 cm$$
Then, Sum of the areas of two circles = $$\pi r_1^2 + \pi r_2^2 = \pi (r_1^2 + r_2^2) = \pi (400+225) = 625\pi$$ which is equal to the area of third square.
$$625\pi = \pi\times25^2$$ is in the form of $$\pi r^2$$.
Therefore, Radius of third square $$r_3 = 25 cm$$
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