# Triangle A has sides of lengths 5 ,4 , and 8 . Triangle B is similar to triangle A and has a side of length 1 . What are the possible lengths of the other two sides of triangle B?

Dec 22, 2017

Possible lengths of other two sides are
Case 1 : 1.25, 2
Case 2 : 0.8, 1.6
Case 3 : 0.5, 0.625

#### Explanation:

Triangles A & B are similar.
Case (1)
$\therefore \frac{1}{4} = \frac{b}{5} = \frac{c}{8}$
$b = \frac{1 \cdot 5}{4} = 1.25$
$c = \frac{1 \cdot 8}{4} = 2$

Possible lengths of other two sides of triangle B are
$9 , 1.25 , 2$

Case (2)
$\therefore \frac{1}{5} = \frac{b}{4} = \frac{c}{8}$
$b = \frac{1 \cdot 4}{5} = 0.8$
$c = \frac{1 \cdot 8}{5} = 1.6$

Possible lengths of other two sides of triangle B are
$9 , 0.8 , 1.6$

Case (3)
$\therefore \frac{1}{8} = \frac{b}{4} = \frac{c}{5}$
$b = \frac{1 \cdot 4}{8} = 0.5$
$c = \frac{1 \cdot 5}{8} = 0.625$

Possible lengths of other two sides of triangle B are
$8 , 0.5 , 0.625$