Gah help please?

Question

Can some please explain how you get the answer to this geometry question?

A rancher has enough material for 271 meters of fence. She knows that a circle maximizes the
area-to-perimeter ratio, but a circular fence is too difficult to construct. She decides to simulate a circle
by building a fence in the shape of a regular polygon with as many sides as possible, but with not less
than five and not more than 15 sides. If she wishes to make each side a length of an even meter, and she
wishes to have no more than 2 meters left over, which regular polygon would you recommend she build,
and how long would each side be?

Answer 1

Well, the maximum number of sides is 15, so try 15:

271/15 = 18 remainder 1

So she should build a regular polygon with 15 sides each of length 18 meters. She will have 1 meter of fence left over.

Sometimes the method of trial and error is good enough.