Area of Triangles · Superchallenge problem

Rectangle $ABCD$ has $AB = 10$ cm and $BC = 6$ cm (corners in order around the rectangle). Point $E$ is the midpoint of side $CD$, and point $F$ is on side $BC$. Triangle $AEF$ has an area of $25$ square centimeters. How long is $BF$, in centimeters?