KöMaL 2013 B4558

The base of a regular four-sided pyramid is the unit square ABCD , its apex is $E$. $P$ is a point on base edge $AB$, and $Q$ is a point on lateral edge $EC$ such that $PQ$ is perpendicular to both $AB$ and $EC$. Furthermore, $AP$:$PB$=6:1. How long are the lateral edges?