In rectangle A B C D, A B=100. Let E be the midpoint of \overline{A D}. Given that line A C and line B E are perpendicular, find the greatest integer less than A D.
In rectangle A B C D, A B=100. Let E be the midpoint of \overline{A D}. Given that line A C and line B E are perpendicular, find the greatest integer less than A D.