# Triangle A has sides of lengths 36 , 42 , and 48 . Triangle B is similar to triangle A and has a side of length 12 . What are the possible lengths of the other two sides of triangle B?

Sep 28, 2016

Other two sides of $B$:
$\textcolor{w h i t e}{\text{XXX}} \left\{14 , 16\right\}$ or
$\textcolor{w h i t e}{\text{XXX}} \left\{10 \frac{2}{7} , 13 \frac{3}{7}\right\}$ or
$\textcolor{w h i t e}{\text{XXX}} \left\{9 , 10 \frac{1}{2}\right\}$

#### Explanation:

Option 1: B's side with length $\textcolor{b l u e}{12}$ corresponds to A's side with length $\textcolor{b l u e}{36}$
Ratio lengths $B : A = 12 : 36 = \frac{1}{3}$
{: ("A's side",rarr,"B's side"), (36,rarr,1/3 * 36=12), (42,rarr,1/3 * 42=14), (48,rarr,1/3 * 48 = 16) :}

Option 2: B's side with length $\textcolor{b l u e}{12}$ corresponds to A's side with length $\textcolor{b l u e}{42}$
Ratio lengths $B : A = 12 : 42 = \frac{2}{7}$
{: ("A's side",rarr,"B's side"), (36,rarr,2/7 * 36=10 2/7), (42,rarr,2/7 * 42=12), (48,rarr,2/7 * 48 = 13 3/7) :}

Option 1: B's side with length $\textcolor{b l u e}{12}$ corresponds to A's side with length $\textcolor{b l u e}{48}$
Ratio lengths $B : A = 12 : 48 = \frac{1}{4}$
{: ("A's side",rarr,"B's side"), (36,rarr,1/4 * 36=9), (42,rarr,1/4 * 42=10 1/2), (48,rarr,1/4 * 48 = 12) :}