# Triangle A has sides of lengths 35 , 25 , and 48 . 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 22, 2017

The other two sides of triangle are
Case 1 : 9.8, 10.64
Case 2 : 5, 7.6
Case 3 : 4.6053, 6.4474

#### Explanation:

Triangles A & B are similar.
Case (1)
$\therefore \frac{7}{25} = \frac{b}{35} = \frac{c}{38}$
$b = \frac{7 \cdot 35}{25} = 9.8$
$c = \frac{7 \cdot 38}{25} = 10.64$

Possible lengths of other two sides of triangle B are
$7 , 9.8 , 10.64$

Case (2)
$\therefore \frac{7}{35} = \frac{b}{25} = \frac{c}{38}$
$b = \frac{7 \cdot 25}{35} = 5$
$c = \frac{7 \cdot 38}{35} = 7.6$

Possible lengths of other two sides of triangle B are
$7 , 5 , 7.6$

Case (3)
$\therefore \frac{7}{38} = \frac{b}{25} = \frac{c}{35}$
$b = \frac{7 \cdot 25}{38} = 4.6053$
$c = \frac{7 \cdot 35}{38} = 6.4474$

Possible lengths of other two sides of triangle B are
$7 , 4.6053 , 6.4474$