2008 AIME I Problem 2

Square AIME has sides of length 10 units. Isosceles triangle GEM has base EM, and the area common to triangle GEM and square AIME is 80 square units. Find the length of the altitude to EM in \triangle GEM.

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.