# Triangle A has sides of lengths 36 , 48 , and 24 . 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?

Mar 6, 2016

In similar triangles the ratios of corresponding sides are the same.

#### Explanation:

So now there are three possibilities, according to which of the sides of triangle A the 4 corresponds to:

If $4 \leftrightarrow 36$ then the ratio=$\frac{36}{4} = 9$ and the other sides will be:
$\frac{48}{9} = 5 \frac{1}{3}$ and $\frac{24}{9} = 2 \frac{2}{3}$

If $4 \leftrightarrow 48$ then the ratio=$\frac{48}{4} = 12$ and the other sides are:
$\frac{36}{12} = 3$ and $\frac{24}{12} = 2$

If $4 \leftrightarrow 24$ the the ratio=$\frac{24}{4} = 6$ and the other sides are:
$\frac{36}{6} = 6$ and $\frac{48}{6} = 8$