# Triangle A has sides of lengths 12 ,1 4, and 11 . Triangle B is similar to triangle A and has a side of length 9 . What are the possible lengths of the other two sides of triangle B?

Dec 21, 2017

Possible lengths of other two sides are
Case 1 : 10.5, 8.25
Case 2 : 7.7143, 7.0714
Case 3 : 9.8182, 11.4545

#### Explanation:

Triangles A & B are similar.
Case (1)
$\therefore \frac{9}{12} = \frac{b}{14} = \frac{c}{11}$
$b = \frac{9 \cdot 14}{12} = 10.5$
$c = \frac{9 \cdot 11}{12} = 8.25$

Possible lengths of other two sides of triangle B are
$9 , 10.5 , 8.25$

Case (2)
$\therefore \frac{9}{14} = \frac{b}{12} = \frac{c}{11}$
$b = \frac{9 \cdot 12}{14} = 7.7143$
$c = \frac{9 \cdot 11}{14} = 7.0714$

Possible lengths of other two sides of triangle B are
$9 , 7.7143 , 7.0714$

Case (3)
$\therefore \frac{9}{11} = \frac{b}{12} = \frac{c}{14}$
$b = \frac{9 \cdot 12}{11} = 9.8182$
$c = \frac{9 \cdot 14}{11} = 11.4545$

Possible lengths of other two sides of triangle B are
$8 , 9.8182 , 11.4545$