Let ABC be an equilateral triangle and P be any point in the interior of the triangle or on the triangle. Use the concept of area to prove that the sum of the distances from P to the three sides of the triangle is constant (the same for all the previously mentioned positions of P). That is, show PE + PD + PF is constant. How is that constant related to the height of the triangle?
Equilateral Triangle-heron-f.jpg