Prove that the sum of the three altitudes of a triangle is less than the sum of the three sides of the triangle.

Asked by Topperlearning User | 11th Aug, 2017, 10:06: AM

Expert Answer:

Of all the line segments drawn to a given line, from a point not on the line, the perpendicular is the shortest,   
                 
AL < AB, BM < BC and CN < CA

Adding the above inequalities,

AL + BM + CN < AB + BC + CA

Hence, the sum of the altitudes is less than the perimeter of the triangle.

Answered by  | 11th Aug, 2017, 12:06: PM