AMC 8 2007 Problem 22

A lemming sits at a corner of a square with side length $10$ meters. The lemming runs $6.2$ meters along a diagonal toward the opposite corner. It stops, makes a $90^{\circ}$ right turn and runs $2$ more meters. A scientist measures the shortest distance between the lemming and each side of the square. What is the average of these four distances in meters? $\textbf{(A)}\ 2 \textbf{(B)}\ 4.5 \textbf{(C)}\ 5 \textbf{(D)}\ 6.2 \textbf{(E)}\ 7$