2006 AIME I Problems/Problem 8
Hexagon is divided into four rhombuses, and as shown. Rhombuses and are congruent, and each has area Let be the area of rhombus Given that is a positive integer, find the number of possible values for
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Let denote the common side length of the rhombi. Let denote one of the smaller interior angles of rhombus . Then Thus is any positive integer on (). . Hence, the number of positive values for is .