Question

Triangle A has sides of lengths `27`, `12`, and `18`. Triangle B is similar to triangle A and has a side of length `3`. What are the possible lengths of the other two sides of triangle B?

Answer 1

There are three solutions, corresponding to assuming each of the 3 sides is similar to the side of length `3`: `(3,4/3,2),(27/4,3,9/2),(9/2,2,3)`

Explanation:

There are three possible solutions, depending on whether we assume the side of length `3` is similar to the side of `27, 12` or `18`.

If we assume it is the side of length `27`, the other two sides would be `12/9=4/3` and `18/9=2`, because `3/27=1/9`.

If we assume it is the side of length `12`, the other two sides would `27/4` and `18/4`, because `3/12=1/4`.

If we assume it is the side of length `18`, the other two sides would be `27/6=9/2` and `12/6=2`, because `3/18=1/6`.

This could be represented in a table.