Question

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?

Answer 1

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:

`\frac{x}{5}=\frac{y}{4}=\frac{4}{3}`

`x=20/3, y=16/3`

Case-2:

`\frac{x}{5}=\frac{y}{3}=\frac{4}{4}`

`x=5, y=3`

Case-3:

`\frac{x}{4}=\frac{y}{3}=\frac{4}{5}`

`x=16/5, y=12/5`

hence, other two possible sides of triangle B are

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