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 \(\triangle GEM\).

(第二十六届AIME1 2008 第2题)