# Triangle A has sides of lengths 24 , 16 , and 20 . 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?

96/5 \ & \ 64/5\ \ or \ \ 24 \ \ & \ \ 20 \ \ \ or \ \ \ 32/3 \ \ & \ \ 40/3

#### Explanation:

Let $x$ & $y$ be two other sides of triangle B similar to triangle A with sides $24 , 16 , 20$.

The ratio of corresponding sides of two similar triangles is same.

Third side $16$ of triangle B may be corresponding to any of three sides of triangle A in any possible order or sequence hence we have following $3$ cases

Case-1:

$\setminus \frac{x}{24} = \setminus \frac{y}{16} = \setminus \frac{16}{20}$

$x = \frac{96}{5} , y = \frac{64}{5}$

Case-2:

$\setminus \frac{x}{24} = \setminus \frac{y}{20} = \setminus \frac{16}{16}$

$x = 24 , y = 20$

Case-3:

$\setminus \frac{x}{16} = \setminus \frac{y}{20} = \setminus \frac{16}{24}$

$x = \frac{32}{3} , y = \frac{40}{3}$

hence, other two possible sides of triangle B are

96/5 \ & \ 64/5\ \ or \ \ 24 \ \ & \ \ 20 \ \ \ or \ \ \ 32/3 \ \ & \ \ 40/3