# Triangle A has sides of lengths 24 , 28 , and 16 . 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?

Nov 19, 2017

Three sets of possible lengths are
1) $7 , \frac{49}{6} , \frac{14}{3}$
2) $7 , 6 , 4$
3) $7 , \frac{21}{2} , \frac{49}{4}$

#### Explanation:

If two triangles are similar, their sides are on the same proportion.
$\frac{A}{a} = \frac{B}{b} = \frac{C}{c}$

Case 1.
$\frac{24}{7} = \frac{28}{b} = \frac{16}{c}$
$b = \frac{28 \cdot 7}{24} = \frac{49}{6}$
$c = \frac{16 \cdot 7}{24} = \frac{14}{3}$

Case 2.
$\frac{28}{7} = \frac{24}{b} = \frac{16}{c}$
$b = 6 , c = 4$

Case 3.
$\frac{16}{7} = \frac{24}{b} = \frac{28}{c}$
$b \frac{21}{2} , c = \frac{49}{4}$