# Triangle A has sides of lengths 32 , 24 , and 28 . Triangle B is similar to triangle A and has a side with a length of 16 . What are the possible lengths of the other two sides of triangle B?

Dec 7, 2017

Possible lengths of the triangle B are

Case (1)
$16 , 18.67 , 21.33$

Case (2)
$16 , 13.71 , 18.29$

Case (3)
$16 , 12 , 14$

#### Explanation:

Triangles A & B are similar.
Case (1)
$\therefore \frac{16}{24} = \frac{b}{28} = \frac{c}{32}$
$b = \frac{16 \cdot 28}{24} = 18.67$
$c = \frac{16 \cdot 32}{24} = 21.33$

Possible lengths of other two sides of triangle B are
$16 , 18.67 , 21.33$

Case (2)
$\therefore \frac{16}{28} = \frac{b}{24} = \frac{c}{32}$
$b = \frac{16 \cdot 24}{28} = 13.71$
$c = \frac{16 \cdot 32}{28} = 18.29$

Possible lengths of other two sides of triangle B are
$16 , 13.71 , 18.29$

Case (3)
$\therefore \frac{16}{32} = \frac{b}{24} = \frac{c}{28}$
$b = \frac{16 \cdot 24}{32} = 12$
$c = \frac{16 \cdot 28}{32} = 14$

Possible lengths of other two sides of triangle B are
$16 , 12 , 14$