Question

AM is a median of a triangle ABC. is AB+BC +CA > 2AM​

Answer 1

Answer:

No 2AM is less than AB+BC+CA.

Answer 2

Answer:

We know, By triangle inequality that sum of the length of any two side of a triangle is always greater than the third side.

Now, In triangle ABM, AB + BM > AM ------ (1)

and In triangle ACM, AC + CM > AM ------(2)

Adding equation (1) and (2), gives,

AB + BM + AC + CM > 2AM

or, AB + BC + CA > 2AM. Where BM + CM = BC.