find PD+PE+PF

For any point P within an equilateral triangle, the sum of the perpendiculars to the three sides is equal to the altitude of the triangle.

 

Let a be the side of the equilateral triangle.

 

In an equilateral triangle, the altitudes, the angle bisectors, the perpendicular bisectors and the medians to each side coincide.

 

Thus, the altitude of the triangle is

Since a = 10 cm (given), we have

Thus, we have,