# Triangle A has sides of lengths 5, 4 , and 3 . Triangle B is similar to triangle A and has a side of length 4 . What are the possible lengths of the other two sides of triangle B?

Other two possible sides of triangle B are

20/3 \ & \ 16/3\ \ or \ \ 5 \ \ & \ \ 3 \ \ \ or \ \ \ 16/5 \ \ & \ \ 12/5

#### Explanation:

Let $x$ & $y$ be two other sides of triangle B similar to triangle A with sides $5 , 4 , 3$.

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

Third side $4$ 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:

$\setminus \frac{x}{5} = \setminus \frac{y}{4} = \setminus \frac{4}{3}$

$x = \frac{20}{3} , y = \frac{16}{3}$

Case-2:

$\setminus \frac{x}{5} = \setminus \frac{y}{3} = \setminus \frac{4}{4}$

$x = 5 , y = 3$

Case-3:

$\setminus \frac{x}{4} = \setminus \frac{y}{3} = \setminus \frac{4}{5}$

$x = \frac{16}{5} , y = \frac{12}{5}$

hence, other two possible sides of triangle B are

20/3 \ & \ 16/3\ \ or \ \ 5 \ \ & \ \ 3 \ \ \ or \ \ \ 16/5 \ \ & \ \ 12/5