Square A I M E has sides of length 10 units. Isosceles triangle G E M has base \overline{E M}, and the area common to triangle G E M and square A I M E is 80 square units. Find the length of the altitude to \overline{E M} in \triangle G E M.
Square A I M E has sides of length 10 units. Isosceles triangle G E M has base \overline{E M}, and the area common to triangle G E M and square A I M E is 80 square units. Find the length of the altitude to \overline{E M} in \triangle G E M.