# Triangle A has sides of lengths 12 , 16 , and 8 . Triangle B is similar to triangle A and has a side with a length of 16 . What are the possible lengths of the other two sides of triangle B?

##### 1 Answer
Sep 28, 2016

The other two sides of $b$ could be
$\textcolor{b l a c k}{\left\{21 \frac{1}{3} , 10 \frac{2}{3}\right\}} \mathmr{and} \textcolor{b l a c k}{\left\{12 , 8\right\}} \mathmr{and} \textcolor{b l a c k}{\left\{24 , 32\right\}}$

#### Explanation:

{: ("sides of "A,,"|",color(blue)(12),"|",color(green)(16),"|",color(cyan)(8)), (,"option",,,,,,), ("possible sides of "B,[1],"|",color(magenta)(16),"|",color(magenta)(16)/color(blue)(12) * color(green)(16) = 21 1/3,"|", color(magenta)(16)/color(blue)(12) * color(cyan)(8) = 10 2/3), (,[2],"|",color(red)(16)/color(green)(16) * color(blue)(12) = 12,"|",color(red)(16),"|",color(red)(16)/color(green)(16) * color(cyan)(8) = 8), (,[3],"|",color(orange)(16)/color(cyan)(8) * color(blue)(12) = 24,"|",color(orange)(16)/color(cyan)(8) * color(green)(16) = 32,"|",color(orange)(16)) :}