Ratio problem.

Level pending

Let \(ABC\) be an equilateral triangle with side length \(a\).Let \(P\) be a point inside this triangle and let \(D\) , \(E\) and \(F\) be the foots of the perpendiculars from \(P\) to \(AB\), \(BC\) and \(AC\).If \(\dfrac{PD+PE+PF}{3a}=k\) then what is \(12k^2\)?

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