Triangle A has sides of lengths 32 , 48 , and 36 . Triangle B is similar to triangle A and has a side of length 8 . What are the possible lengths of the other two sides of triangle B?

Oct 18, 2017

The other two sides are 12, 9 respectively.

Explanation:

Since the two triangles are similar, corresponding sides are in the same proportion.
If the $\Delta$s are ABC & DEF,
$\frac{A B}{D E} = \frac{B C}{E F} = \frac{C A}{F D}$

$\frac{32}{8} = \frac{48}{E F} = \frac{36}{F D}$
$E F = \frac{48 \cdot 8}{32} = 12$
$F D = \frac{36 \cdot 8}{32} = 9$

Oct 18, 2017

The other two sides of triangle $B$ could have lengths:

$12$ and $9$

$\frac{16}{3}$ and $6$

$\frac{64}{9}$ and $\frac{96}{9}$

Explanation:

Given triangle A has sides of lengths:

$32 , 48 , 36$

We can divide all these lengths by $4$ to get:

$8 , 12 , 9$

or by $6$ to get:

$\frac{16}{3} , 8 , 6$

or by $\frac{9}{2}$ to get:

$\frac{64}{9} , \frac{96}{9} , 8$

So the other two sides of triangle $B$ could have lengths:

$12$ and $9$

$\frac{16}{3}$ and $6$

$\frac{64}{9}$ and $\frac{96}{9}$