Question

show that perimeter of a triangle is greater than the sum of three medians​

Answer 1

SOLUTION

In this question it is given that we have to prove that the perimeter of a triangle is always greater that its sum of three medians.

For solving this let us draw a triangle ABC having three medians D,E and F.

Now,

TO PROVE: AB+BC+CA>AD+BE+CF

PROOF

We know,

" SUM OF ANY TWO SIDES OF A TRIANGLE IS ALWAYS GRATER THAN TWICE ITS MEDIAN"

Therefore,

AB+BC>2AD.....(1)

BC+CA>2BE.....(2)

AB+CA>2CF.....(3)

On adding Equations,1,2 and 3,We get

AB+BC+CA>AD+BE+CF

Hence , it is proved.