Hexagon slices

Weekly Problem 37 - 2007
This regular hexagon has been divided into four trapezia and one hexagon.... what is the ratio of the lengths of sides p, q and r?
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Problem

This regular hexagon has been divided into four trapezia and one hexagon. If each of the five sections has the same perimeter, what is the ratio of the lengths $p$, $q$ and $r$?

Image
Hexagon Slices

If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.