# Triangle A has sides of lengths 32 , 36 , 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?

Feb 13, 2018

Case 1 : Delta B = color(green)(8, 18, 16

case 2 : Delta B = color(brown)(8, 9, 4

Case 3 : Delta B = color(blue)(8, 32/9. 64/9

#### Explanation:

Case 1 : side 8 of triangle B corresponding to side 16 in triangle A

$\frac{8}{16} = \frac{b}{36} = \frac{c}{32}$

$b = \frac{{\cancel{36}}^{\textcolor{g r e e n}{18}} \cdot \cancel{8}}{\cancel{16}} ^ \textcolor{red}{\cancel{2}}$

#b = 18,

$c = \frac{{\cancel{32}}^{\textcolor{g r e e n}{16}} \cdot \cancel{8}}{\cancel{16}} ^ \textcolor{red}{\cancel{2}}$

$c = 16$

Similarly,Case 2 : side 8 of triangle B corresponding to side 32 in triangle A

$\frac{8}{32} = \frac{b}{36} = \frac{c}{16}$

$b = 9 , c = 4$

Case 3 : side 8 of triangle B corresponding to side 36 in triangle A

$\frac{8}{36} = \frac{b}{16} = \frac{c}{32}$

$b = \frac{32}{9} , c = \frac{64}{9}$