# Triangle A has sides of lengths 32 , 48 , and 64 . 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?

Triangle A:$32 , 48 , 64$
Triangle B: $8 , 12 , 16$
Triangle B:$\frac{16}{3} , 8 , \frac{32}{3}$
Triangle B:$4 , 6 , 8$

#### Explanation:

Given Triangle A:$32 , 48 , 64$
Let triangle B have sides x, y, z then, use ratio and proportion to find the other sides.
If the first side of triangle B is x=8, find y, z

solve for y:

$\frac{y}{48} = \frac{8}{32}$

$y = 48 \cdot \frac{8}{32}$

$y = 12$
`
solve for z:
$\frac{z}{64} = \frac{8}{32}$

$z = 64 \cdot \frac{8}{32}$
$z = 16$
Triangle B: $8 , 12 , 16$

the rest are the same for the other triangle B

if the second side of triangle B is y=8, find x and z

solve for x:
$\frac{x}{32} = \frac{8}{48}$
$x = 32 \cdot \frac{8}{48}$
$x = \frac{32}{6} = \frac{16}{3}$

solve for z:
$\frac{z}{64} = \frac{8}{48}$
$z = 64 \cdot \frac{8}{48}$
$z = \frac{64}{6} = \frac{32}{3}$

Triangle B:$\frac{16}{3} , 8 , \frac{32}{3}$
~~~~~~~~~~~~~~~~~~~~

If the third side of triangle B is z=8, find x and y
$\frac{x}{32} = \frac{8}{64}$
$x = 32 \cdot \frac{8}{64}$
$x = 4$

solve for y:

$\frac{y}{48} = \frac{8}{64}$

$y = 48 \cdot \frac{8}{64}$
$y = 6$

Triangle B:$4 , 6 , 8$

God bless....I hope the explanation is useful.