Question:
What is the diameter of a circle whose area is equal to the sum of the areas of two circles of diameters 10 cm and 24 cm?
Solution:
Let the diameter of the required circle be d.
Now, Area of required circle = Area of circle having diameter 10 cm + Area of circle having diameter 24 cm
$\Rightarrow \pi\left(\frac{d}{2}\right)^{2}=\pi\left(\frac{10}{2}\right)^{2}+\pi\left(\frac{24}{2}\right)^{2}$
$\Rightarrow\left(\frac{d}{2}\right)^{2}=25+144$
$\Rightarrow\left(\frac{d}{2}\right)^{2}=13^{2}$
$\Rightarrow \frac{d}{2}=13$
$\Rightarrow d=26 \mathrm{~cm}$
Hence, the diameter of the of the circle is 26 cm.