# A Rectangle inside a Triangle!

Geometry Level 5

Given a $$\Delta ABC$$ with $$DE \parallel BC$$, with $$D \in AB$$ and $$E \in AC$$. Drop perpendiculars from $$D$$ and $$E$$ to $$BC$$, meeting $$BC$$ at $$F$$ and $$K$$ respectively.

If $$\dfrac{[ABC]}{[DEKF]} = \dfrac{32}{7}$$, find the value of $$\dfrac{|AD|}{|BD|}$$.

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