The side lengths of a triangle are consecutive integers.
The largest interior angle is twice the smallest.

What are the side lengths of the triangle?

(In reply to To Jer and a Confirmation by brianjn)

All 3 solutions compare sides to angles -- how could they not?
The problem gives a lot of info but all the solutions do the same thing:

Create two different relations between sides and angles then find a way to combine them into a single equation involving just sides.

Charlies computer solution appears to show something interesting as well:  Only the 4,5,6, triangle has an angle ratio that is rational.  I don't expect a proof there to be easy so that will remain an observation.

Posted by Jer on 2009-03-06 13:24:51