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Leya [2.2K]
3 years ago
10

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 cir

cle.
Mathematics
1 answer:
zlopas [31]3 years ago
7 0
   
\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}} }



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