Question

prove that the sum of altitudes is less than the sum of the sides of the triangle

Answer 1

In triangle APB, AP is a median.

Angle APB is greater than angle ABP. so angles opposite to greater side is longer.

therefore AB is greater than AP. hence proved that in triangle APB the side of the triangle is more than the median or altitude AP of the triangle.

In the same manner the other triangles can also be proved.

I am not describing the whole answer because practice makes a man perfect!!!

Its very easy. It is just in different triangles.

Hope it helps!!!