MathDB
Pentagon Problem

Source: AIME 2004 Alt. #13

November 17, 2005
ratiogeometrynumber theoryrelatively prime

Problem Statement

Let ABCDEABCDE be a convex pentagon with AB∥CEAB\parallel CE, BC∥ADBC\parallel AD, AC∥DEAC\parallel DE, ∠ABC=120∘\angle ABC=120^\circ, AB=3AB=3, BC=5BC=5, and DE=15DE=15. Given that the ratio between the area of triangle ABCABC and the area of triangle EBDEBD is m/nm/n, where mm and nn are relatively prime positive integers, find m+nm+n.
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