# Triangle A has sides of lengths 12 , 9 , and 8 . Triangle B is similar to triangle A and has a side with a length of 16 . What are the possible lengths of the other two sides of triangle B?

Dec 22, 2017

The other two sides of triangle are
Case 1 : 12, 10.6667
Case 2 : 21.3333, 14.2222
Case 3 : 24, 18

#### Explanation:

Triangles A & B are similar.
Case (1)
$\therefore \frac{16}{12} = \frac{b}{9} = \frac{c}{8}$
$b = \frac{16 \cdot 9}{12} = 12$
$c = \frac{16 \cdot 8}{12} = 10.6667$

Possible lengths of other two sides of triangle B are
$9 , 12 , 10.6667$

Case (2)
$\therefore \frac{16}{9} = \frac{b}{12} = \frac{c}{8}$
$b = \frac{16 \cdot 12}{9} = 21.3333$
$c = \frac{16 \cdot 8}{9} = 14.2222$

Possible lengths of other two sides of triangle B are
$9 , 21.3333 , 14.2222$

Case (3)
$\therefore \frac{16}{8} = \frac{b}{12} = \frac{c}{9}$
$b = \frac{16 \cdot 12}{8} = 24$
$c = \frac{16 \cdot 9}{8} = 18$

Possible lengths of other two sides of triangle B are
$8 , 24 , 18$