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 20090306 13:24:51 