Question

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?

Answer 1

`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:

`\frac{x}{24}=\frac{y}{16}=\frac{16}{20}`

`x=96/5, y=64/5`

Case-2:

`\frac{x}{24}=\frac{y}{20}=\frac{16}{16}`

`x=24, y=20`

Case-3:

`\frac{x}{16}=\frac{y}{20}=\frac{16}{24}`

`x=32/3, y=40/3`

hence, other two possible sides of triangle B are

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