Question 161
From a point inside the equilateral triangle $ABC$ are drawn perpendicular lines to the sides $AB$, $BC$ and $CA$. The lengths of these lines are $m$, $n$, $p$ and the length of the side of the triangle $ABC$ is equal to $a$. Find the ratio of the areas of the triangle $ABC$ and the triangle formed with the points of the intersection of the perpendicular lines and sides.