# Triangle A has sides of lengths 1 ,4 , and 4 . Triangle B is similar to triangle A and has a side of length 3 . What are the possible lengths of the other two sides of triangle B?

Dec 1, 2017

The possible lengths of the DEF triangle are
$\textcolor{red}{3 , 12 , 12}$ & $\textcolor{b l u e}{\frac{3}{4} , 3 , 3}$

#### Explanation:

Since the two triangles are similar, their corresponding sides are proportional.
Let the two triangles be ABC & DEF.

Then $\frac{a}{d} = \frac{b}{e} = \frac{c}{f}$
$a = 1 , b = 4 , c = 4$

If $d = 3$, then
$\frac{1}{3} = \frac{4}{e} = \frac{4}{f}$
$\therefore e = 12 , f = 12$

If $e = 3$, then
$\frac{4}{3} = \frac{1}{d} = \frac{4}{f}$
$\therefore d = \frac{3}{4} , f = 3$

The possible lengths of the DEF triangle are
$\textcolor{red}{3 , 12 , 12}$ & $\textcolor{b l u e}{\frac{3}{4} , 3 , 3}$