# Triangle A has sides of lengths 36 ,24 , and 16 . 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: 36, 24, 16
Triangle B: $8 , \frac{16}{3} , \frac{32}{9}$
Triangle B: $12 , 8 , \frac{16}{3}$
Triangle B: $18 , 12 , 8$

#### Explanation:

From the given
Triangle A: 36, 24, 16

Use ratio and proportion

Let x, y, z be the sides respectively of triangle B proportional to triangle A

Case 1.

If x=8 in triangle B, solve y
$\frac{y}{24} = \frac{x}{36}$

$\frac{y}{24} = \frac{8}{36}$
$y = 24 \cdot \frac{8}{36}$
$y = \frac{16}{3}$

If x=8 solve z
$\frac{z}{16} = \frac{x}{36}$
$\frac{z}{16} = \frac{8}{36}$
$z = 16 \cdot \frac{8}{36}$
$z = \frac{32}{9}$
~~~~~~~~~~~~~~~~~~~~~~~
Case 2.

if y=8 in triangle B solve x
$\frac{x}{36} = \frac{y}{24}$
$\frac{x}{36} = \frac{8}{24}$
$x = 36 \cdot \frac{8}{24}$
$x = 12$

If y=8 in triangle B solve z
$\frac{z}{16} = \frac{y}{24}$
$\frac{z}{16} = \frac{8}{24}$
$z = 16 \cdot \frac{8}{24}$
$z = \frac{16}{3}$
~~~~~~~~~~~~~~~~~~~~~~~
Case 3.

if z=8 in triangle B, solve x
$\frac{x}{36} = \frac{z}{16}$
$\frac{x}{36} = \frac{8}{16}$
$x = 36 \cdot \frac{8}{16}$
$x = 18$

if z=8 in triangle B, solve y
$\frac{y}{24} = \frac{z}{16}$
$\frac{y}{24} = \frac{8}{16}$
$y = 24 \cdot \frac{8}{16}$
$y = 12$

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