# Triangle A has sides of lengths 27 , 12 , and 18 . Triangle B is similar to triangle A and has a side of length 3 . What are the possible lengths of the other two sides of triangle B?

Feb 16, 2016

There are three solutions, corresponding to assuming each of the 3 sides is similar to the side of length $3$: $\left(3 , \frac{4}{3} , 2\right) , \left(\frac{27}{4} , 3 , \frac{9}{2}\right) , \left(\frac{9}{2} , 2 , 3\right)$

#### Explanation:

There are three possible solutions, depending on whether we assume the side of length $3$ is similar to the side of $27 , 12$ or $18$.

If we assume it is the side of length $27$, the other two sides would be $\frac{12}{9} = \frac{4}{3}$ and $\frac{18}{9} = 2$, because $\frac{3}{27} = \frac{1}{9}$.

If we assume it is the side of length $12$, the other two sides would $\frac{27}{4}$ and $\frac{18}{4}$, because $\frac{3}{12} = \frac{1}{4}$.

If we assume it is the side of length $18$, the other two sides would be $\frac{27}{6} = \frac{9}{2}$ and $\frac{12}{6} = 2$, because $\frac{3}{18} = \frac{1}{6}$.

This could be represented in a table.