# Triangle A has sides of lengths 54 , 44 , and 32 . Triangle B is similar to triangle A and has a side of length 4 . What are the possible lengths of the other two sides of triangle B?

Sep 10, 2016

Because the problem doesn't state which side in Triangle A corresponds to the side of length 4 in triangle B, there are multiple answers.

If the side with length 54 in A corresponds to 4 in B:

Find the proportionality constant:

$54 K = 4$
$K = \frac{4}{54} = \frac{2}{27}$

The 2nd side $= \frac{2}{27} \cdot 44 = \frac{88}{27}$
The3rd side$= \frac{2}{27} \cdot 32 = \frac{64}{27}$

If the side with length 44 in A corresponds to 4 in B:

$44 K = 4$
$K = \frac{4}{44} = \frac{1}{11}$

The 2nd side$= \frac{1}{11} \cdot 32 = \frac{32}{11}$
The 3rd side$= \frac{1}{11} \cdot 54 = \frac{54}{11}$

If the side with length 32 in A corresponds to 4 in B:

$32 K = 4$
$K = \frac{1}{8}$

The 2nd side$= \frac{1}{8} \cdot 44 = \frac{11}{2}$
The 3rd side$= \frac{1}{8} \cdot 54 = \frac{27}{4}$