Black book 6

Geometry Level 4

Let \(ABC\) be a given triangle.Points \(D\) and \(E\) are on sides \(AB\) and \(AC\) respectively and point \(F\) is on line segment \(DE\).Let \(\dfrac{AD}{AB}=0.5\),\(\dfrac{AE}{AC}=.6\),\(\dfrac{DF}{DE}=.8\) Let area of \(\Delta BDF = \Delta_1\), area of \(\Delta CEF=\Delta_2\) and area of \(\Delta ABC=\Delta\)

  • \(\dfrac{\Delta_1}{\Delta}\) is equal to \(P\)

  • \(\dfrac{\Delta_2}{\Delta}\) is equal to \(Q\)

Find \({2P+10Q}\).


Bones:Generalize it.

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