Question

The radius of one circle is three the time radius of another circle. The sum of their areas is 12pi. Find the radius of each circle.

Answer 1

   
$\displaystyle\\ \begin{cases} R_1 = 3R_2\\ \pi R_1^2 +\pi R_2^2=12\pi ~~~\Big|~~:\pi \end{cases} \\ \\ \begin{cases} R_1 = 3R_2\\ R_1^2 + R_2^2=12 \end{cases} \\ \\ (3R_2)^2+ R_2^2=12 \\ \\ 9R_2^2 + R_2^2=12 \\ \\ 10R_2^2=12\\\\ R_2^2 = \frac{12}{10} = \frac{6}{5} \\ \\ R_2 = \boxed{\sqrt{\frac{6}{5}} } \\ \\ R_1 = \boxed{3\sqrt{\frac{6}{5}} }$