# Triangle A has sides of lengths 48 ,36 , and 54 . Triangle B is similar to triangle A and has a side of length 5 . What are the possible lengths of the other two sides of triangle B?

May 14, 2017

Possible sides of $\triangle B$:
$\textcolor{w h i t e}{\text{XXX}} \left\{5 , 3 \frac{3}{4} , 5 \frac{5}{8}\right\}$ or
$\textcolor{w h i t e}{\text{XXX}} \left\{6 \frac{2}{3} , 5 , 7 \frac{1}{2}\right\}$ or
$\textcolor{w h i t e}{\text{XXX}} \left\{4 \frac{4}{9} , 3 \frac{1}{3} , 5\right\}$

#### Explanation:

Suppose the sides of $\triangle A$ are
$\textcolor{w h i t e}{\text{XXX}} {P}_{A} = 48 , {Q}_{A} = 36 , \mathmr{and} {R}_{A} = 54$
with corresponding sides of $\triangle B$:
$\textcolor{w h i t e}{\text{XXX}} {P}_{B} , {Q}_{B} , \mathmr{and} {R}_{B}$

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