VTRMC 2017 Problem 4

Let $P$ be an interior point of a triangle of area $T$ . Through the point $P$ , draw lines parallel to the three sides, partitioning the triangle into three triangles and three parallelograms. Let $a$ , $b$ and $c$ be the areas of the three triangles. Prove that $\sqrt { T } = \sqrt { a } + \sqrt { b } + \sqrt { c }$ .