The sum of three altitudes of a triangle is
The sides are AB, BC and CA. The altitudes are AD, BE and CF.
Being the sides of triangles as altitudes then sides of triangles have to be the hypotenuse.
It is clear that hypotenuse is always greater than any one of the other sides
So AB>AD and BC>BE and CA>CF
Now adding AB+BC+CA > AD+BE+CF
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