# 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 \(\dfrac{|AD|}{|BD|}\).