Question

Prove that in a triangle

the sum of altitudes is less than the

sum of sides of a triangle

Answer 1

Here's your answer..

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Solution:-

Let AD ,CF and BE the altitude of the triangle.

Since we know that,
Line segment drawn from a point outside a line to line,the Perpendicular is shortest.

So,

=>AD<AC , BE<BC , CF <AB

=>AD+BE+CF < AC +BC +AB

Hence,it is proved that sum of three altitudes of the triangle is less than sides of triangle.

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#See the attached also..

Hope it helps you...