Area of Triangles · Superchallenge problem

Square $ABCD$ has sides of $10$ m (corners in order around the square). Two straight paths start at corner $A$: one ends at point $E$ on side $BC$, the other at point $F$ on side $CD$. The paths split the square into three pieces with equal areas. How long is $BE$, in meters? Give your answer as an improper fraction.