2009 AIME II Problem 3

In rectangle ABCD, AB=100. Let E be the midpoint of \overline{AD}. Given that line AC and line BE are perpendicular, find the greatest integer less than AD.

Leading zeroes must be inputted, so if your answer is 34, then input 034

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.