2004 AIME II Problems/Problem 13

Problem

Let $ABCDE$ be a convex pentagon with $AB || CE, BC || AD, AC || DE, \angle ABC=120^\circ, AB=3, BC=5,$ and $\displaystyle DE = 15.$ Given that the ratio between the area of triangle $ABC$ and the area of triangle $EBD$ is $m/n,$ where $m$ and $n$ are relatively prime positive integers, find $m+n.$

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2004 AIME II Problems/Problem 13

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