# Triangle A has sides of lengths 12 ,24 , and 16 . Triangle B is similar to triangle A and has a side of length 8 . What are the possible lengths of the other two sides of triangle B?

Apr 22, 2016

Three possibilities are there. Three sides are either (A) $8 , 16$ and $10 \frac{2}{3}$ or (B) $4 , 8$ and $5 \frac{1}{3}$ or (C) $6 , 12$ and $8$.

#### Explanation:

The sides of triangle A are $12 , 24$ and $16$ and triangle B is similar to triangle A with a side of length $8$. Let other two sides be $x$ and $y$. Now, we have three possibilities. Either

$\frac{12}{8} = \frac{24}{x} = \frac{16}{y}$ then we have $x = 16$ and $y = 16 \times \frac{8}{12} = \frac{32}{3} = 10 \frac{2}{3}$ i.e. three sides are $8 , 16$ and $10 \frac{2}{3}$

or $\frac{12}{x} = \frac{24}{8} = \frac{16}{y}$ then we have $x = 4$ and $y = 16 \times \frac{8}{24} = \frac{16}{3} = 5 \frac{1}{3}$ i.e. three sides are $4 , 8$ and $5 \frac{1}{3}$

or $\frac{12}{x} = \frac{24}{y} = \frac{16}{8}$ then we have $x = 6$ and $y = 12$ i.e. three sides are $6 , 12$ and $8$