Given that \( P \) is a point inside an equilateral triangle of side 2016 units. Find the sum of the lengths of the perpendiculars drawn from \( P \) to the sides.

If the answer will be in the form of \( a\sqrt{b} \) for positive integers \(a\) and \(b\) with \( b\) square free, type your answer as \( a+ b \).

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