Question

Which set of side lengths form a right triangle?

Answer 1

Since we don't want to use the Pythagorean Theorem on all of these, first we look for some Pythagorean Triples. Its very helpful to know some of the common ones, so here's a list:

3, 4, 5
5, 12, 13
7, 24, 25
8, 15, 17

So we either look for these or a multiple of these numbers.

The last one is the only one that fits because 15, 20, 25 is a multiple of the triple 3, 4, 5 by multiplying all of them by 5. 

Thus, 15, 20, 25 forms a right triangle.