# Triangle A has sides of lengths 51 , 45 , and 54 . Triangle B is similar to triangle A and has a side of length 9 . What are the possible lengths of the other two sides of triangle B?

Apr 30, 2018

9, 8.5 & 7.5
9, 10.2 & 10.8
7.941, 9 & 9.529

#### Explanation:

If 9 is the longest side then the multiplier wold be $\frac{54}{9} = 6$

$\frac{51}{6} = 8.5$. $\frac{45}{6} = 7.5$

If 9 is the shortest side then the multiplier would be $\frac{45}{9} = 5$

$\frac{51}{5} = 10.2$, $\frac{54}{5} = 10.8$

If 9 is the middle side then the multiplier would be $\frac{51}{9} = 5 \frac{2}{3}$

$\frac{45}{5 \frac{2}{3}} = 7.941$, $\frac{54}{5 \frac{2}{3}} = 9.529$