Half Way Points

Geometry Level 5

As shown, \(ABC\) is a right angle triangle with \(\angle A = 90^\circ\) and \(BC=100\). \(D\) is the midpoint of \(AB\) and equation of \(CD\) is \(y=3x+4\); \(E\) is the midpoint of \(AC\) and equation of \(BE\) is \(y=6-5x\). Given that the area of triangle \(ABC\) is \(\dfrac{p}{q}\), where \(p\) and \(q\) are coprime positive integers, find \(p+q\).

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