# 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 $\triangle B$:
$\textcolor{w h i t e}{\text{XXX}} {P}_{B} , {Q}_{B} , \mathmr{and} {R}_{B}$

{: ("Given:",,,,,), (,P_A,color(white)("xx"),Q_A,color(white)("xx"),R_A), (,48,color(white)("xx"),36,color(white)("xx"),54), ("Possibilities:",,,,,), (,P_B,color(white)("xx"),Q_B,color(white)("xx"),R_B), (,5,color(white)("xx"),5/48 * 36=3 3/4,color(white)("xx"),5/48*54=5 5/8), ("or",5/36 * 48=6 2/3,color(white)("xx"),5,color(white)("xx"),5/36*54=7 1/2), ("or",5/54*48=4 4/9,color(white)("xx"),5/54*36=3 1/3,color(white)("xx"),5) :}