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Problem of the Day #122: I like pentagons July 19, 2011

Posted by Mitchell in : potd , trackback

Let ABCDE be a pentagon with $AB \parallel CE$, $BC \parallel AD$, $AC \parallel DE$, $\angle ABC=120^\circ$, $AB=6$, $BC=10$, and $DE = 30$. The ratio of the area of $\triangle ABC$ to the area of $\triangle EBD$ can be expressed in the form $\frac{a}{b}$, where $a$ and $b$ are relatively prime positive integers. Compute $a+b$.

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