# 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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