# The next year

Geometry Level 3

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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