# Triangle A has sides of lengths 27 , 15 , and 21 . 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?

The sides of Triangle B are either 9, 5, or 7 times smaller.

#### Explanation:

Triangle A has lengths of 27, 15, and 21.

Triangle B is similar to A and has one side of side 3. What are the other 2 side lengths?

The side of 3 in Triangle B could be the similar side to Triangle A's side of 27 or 15 or 21. So the sides of A could be $\frac{27}{3}$ of B, or $\frac{15}{3}$ of B, or $\frac{21}{3}$ of B. So let's run through all the possibilities:

$\frac{27}{3}$ or 9 times smaller: $\frac{27}{9} = 3 , \frac{15}{9} = \frac{5}{3} , \frac{21}{9} = \frac{7}{3}$

$\frac{15}{3}$ or 5 times smaller: $\frac{27}{5} , \frac{15}{5} = 3 , \frac{21}{5}$

$\frac{21}{3}$ or 7 times smaller: $\frac{27}{7} , \frac{15}{7} , \frac{21}{7} = 3$