# Triangle A has sides of lengths 12 ,17 , and 11 . 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?

Dec 21, 2017

Possible lengths of other two sides of triangle B are
Case 1 : 11.3333, 7.3333
Case 2 : 5.6471, 5.1765
Case 3 : 8.7273, 12.3636

#### Explanation:

Triangles A & B are similar.
Case (1)
$\therefore \frac{8}{12} = \frac{b}{17} = \frac{c}{11}$
$b = \frac{8 \cdot 17}{12} = 11.3333$
$c = \frac{8 \cdot 11}{12} = 7.3333$

Possible lengths of other two sides of triangle B are
$8 , 11.3333 , 7.3333$

Case (2)
$\therefore \frac{8}{17} = \frac{b}{12} = \frac{c}{11}$
$b = \frac{8 \cdot 12}{17} = 5.6471$
$c = \frac{8 \cdot 11}{17} = 5.1765$

Possible lengths of other two sides of triangle B are
$8 , 7.3333 , 5.1765$

Case (3)
$\therefore \frac{8}{11} = \frac{b}{12} = \frac{c}{17}$
$b = \frac{8 \cdot 12}{11} = 8.7273$
$c = \frac{8 \cdot 17}{11} = 12.3636$

Possible lengths of other two sides of triangle B are
$8 , 8.7273 , 12.3636$