Question

Show that the sum of the three altitudes of a triangle is less than the sum of three sides of the triangle ??​

Answer 1

Let AL, BM, CN be the three altitudes of triangle ABC.

We know that, of all line segments drawn from a point outside a line, the perpendicular is the shortest.

AL<AB, BM<BC and CN<AC

AL + BM + CN < AB +BC + AC

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