# Triangle A has sides of lengths 81 , 45 , and 66 . Triangle B is similar to triangle A and has a side of length 7 . What are the possible lengths of the other two sides of triangle B?

Dec 21, 2017

Length of other two sides are
Case 1 : 3.8889, 5.7037
Case 2 : 12.6, 10.2667
Case 3 : 4.7727, 8.5909

#### Explanation:

Triangles A & B are similar.
Case (1)
$\therefore \frac{7}{81} = \frac{b}{45} = \frac{c}{66}$
$b = \frac{7 \cdot 45}{81} = 3.8889$
$c = \frac{7 \cdot 66}{81} = 5.7037$

Possible lengths of other two sides of triangle B are
$7 , 3.8889 , 5.7037$

Case (2)
$\therefore \frac{7}{45} = \frac{b}{81} = \frac{c}{66}$
$b = \frac{7 \cdot 81}{45} = 12.6$
$c = \frac{7 \cdot 66}{45} = 10.2667$

Possible lengths of other two sides of triangle B are
$7 , 12.6 , 10.2667$

Case (3)
$\therefore \frac{7}{66} = \frac{b}{45} = \frac{c}{81}$
$b = \frac{7 \cdot 45}{66} = 4.7727$
$c = \frac{7 \cdot 81}{66} = 8.5909$

Possible lengths of other two sides of triangle B are
$7 , 4.7727 , 8.5909$