Question 61
Let $ABCD$ be a square with the side-length $10$. Let $E$ and $F$ be the points on the sides $BC$ and $AD$ respectively, so that $ABEF$ is a rectangle. The rectangle $KLMN$ is such that its vertices $K$, $L$, $M$ and $N$ belong to the segments $CD$, $DF$, $FE$ and $EC$ respectively. It turns out that the rectangles $ABEF$ and $KLMN$ are equal, and $AB = MN$. Determine the length of the segment $AL$.
Fig. 1
Fig. 1