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Integer Side Lengths (Posted on 2009-03-05) Difficulty: 2 of 5
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?

See The Solution Submitted by Bractals    
Rating: 3.0000 (1 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
re: To Jer and a Confirmation Comment 8 of 8 |
(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

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