Question

Prove that sum of all sides of the triangle is greater than sum of its corresponding altitudes​

Answer 1

Answer:

Step-by-step explanation:

Let there be a triangle ABC with its altitudes D, E and F from vertices A, B and C respectively.

The altitudes form a right angled triangle at their corresponding bases. Also in a right angled triangle the hypotenuse is the longest side. Taking the right angles formed by the altitudes and the sides as the hypotenuse, we observe in each triangle, the side forms the longest side, i.e.

In triangle ABD, AB is the longest side.

In triangle ACF, AC is the longest side.

In triangle CBE, BC is the longest side.

So, adding all these three sides, we find that the perimeter of a triangle is greater than the sum of its three altitudes.

Hence proved.

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