Question

Triangle A has sides of lengths `27`, `15`, and `21`. 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

The sides of Triangle B are either 9, 5, or 7 times smaller.

Explanation:

Triangle A has lengths of 27, 15, and 21.

Triangle B is similar to A and has one side of side 3. What are the other 2 side lengths?

The side of 3 in Triangle B could be the similar side to Triangle A's side of 27 or 15 or 21. So the sides of A could be `27/3` of B, or `15/3` of B, or `21/3` of B. So let's run through all the possibilities:

`27/3` or 9 times smaller: `27/9 = 3, 15/9 = 5/3, 21/9 = 7/3`

`15/3` or 5 times smaller: `27/5, 15/5 = 3, 21/5`

`21/3` or 7 times smaller: `27/7, 15/7, 21/7 = 3`