Ratio problem.

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 $12k^2$ ?