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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