A problem by Sherry Sarkar

Level pending

In Triangle \(ABC\), \(AB\) = 48 , \(BC\) = 27 , \(AC\) = 32. \(D\) is on \(AC\) such that \(AD\) = 20 and \(E\) is on \(AB\) such that \(AE\) = 18. The ratio of the area of triangle \(ADE\) to the area of quadrilateral \(BEDC\) can be expressed as \(\frac{a}{b}\).

What is \(a + b\)?

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