Question

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

Answer 1

We have to prove that the sum of three altitude of the triangle is less than the sum of its sides.

In we have

, and

We have to prove

As we know perpendicular line segment is shortest in length

Since

So ........(1)

And

........(2)

Adding (1) and (2) we get

........(3)

Now, so

.......(4)

And again, this implies that

........(5)

Adding (3) & (4) and (5) we have

HenceProved.