# Triangle A has sides of lengths 7 ,4 , and 8 . 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?

##### 1 Answer
Dec 7, 2017

Possible lengths of the triangle B are

Case (1)
$9 , 15.75 , 18$

Case (2)
$9 , 5.14 , 10.29$

Case (3)
$9 , 4.5 , 7.875$

#### Explanation:

Triangles A & B are similar.
Case (1)
$\therefore \frac{9}{4} = \frac{b}{7} = \frac{c}{8}$
$b = \frac{9 \cdot 7}{4} = 15.75$
$c = \frac{9 \cdot 8}{4} = 18$

Possible lengths of other two sides of triangle B are
$9 , 15.75 , 18$

Case (2)
$\therefore \frac{9}{7} = \frac{b}{4} = \frac{c}{8}$
$b = \frac{9 \cdot 4}{7} = 5.14$
$c = \frac{9 \cdot 8}{7} = 10.29$

Possible lengths of other two sides of triangle B are
$9 , 5.14 , 10.29$

Case (3)
$\therefore \frac{9}{8} = \frac{b}{4} = \frac{c}{7}$
$b = \frac{9 \cdot 4}{8} = 4.5$
$c = \frac{9 \cdot 7}{8} = 7.875$

Possible lengths of other two sides of triangle B are
$9 , 4.5 , 7.875$