Many of us are familiar with the 3, 4, 5 right triangle, and maybe the 5, 12, 13. Do you know any others? Is there a pattern to these triples?

Investigate the relationships between the lengths of the sides of the triangles that belong to this set.

The first url above is a write-up of this problem from the Math Assessment Project and includes teacher notes and sample student work. The second url is a write-up of teachers exploring this task, including ideas on how to introduce it and photographs of their reasoning.