A Pre-RMO question! -25

Geometry Level 2

In a rectangle ABCDABCD, AB=5cm,BC=3cm\overline{AB}=5cm,\overline{BC}=3cm. Points F and G lies on line segment CD\overline{CD} such that DF=1cm,GC=2cm\overline{DF}=1cm,\overline{GC}=2cm. Lines AF\overline{AF} and BG\overline{BG} when joined and extended intersects at EE. If the area of AEB\triangle AEB is mncm2\dfrac{m}{n}cm^2 where mZ+;nZ+;gcd(m,n)=1m\in Z^+;n\in Z^+;\gcd(m,n)=1 then find m+nm+n

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