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Square and Isosceles Triangle

Source: AIME 2008I Problem 2

March 23, 2008
AMCAIMEgeometrytrapezoid

Problem Statement

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