There is a decagon with eight 150 degree angles and two 120 degree angles. The lengths of its sides are a set of ten consecutive integers. Maximize the length of its longest side.

(In reply to thoughts by Charlie)

Not only is is impossible to have both left and right to have exactly one sqrt(3)/2 vertical drop multipliers each, but also they cannont have exactly one .5 multiplier each, as that would entail the horizontal direction having exactly one sqrt(3)/2 multiplier, resulting in an irrational difference between the top and bottom parallel faces.

 

Posted by Charlie on 2005-01-31 00:19:02