Question

Question 3
AM is a median of a triangle ABC. Is AB + BC + CA > 2AM? (Consider the sides of triangles ABM and AMC.)

Answer 1

Since, the sum of lengths of any two sides in a triangle should be greater than the length of third side.
Therefore, In $\Delta$ ABM, AB + BM > AM ……….(i)
In $\Delta$ AMC, AC + MC > AM ……….(ii)
Adding eq. (i) and(ii),
AB + BM + AC + MC > AM +AM
$\Rightarrow$ AB + AC + (BM + MC) >2AM
$\Rightarrow$ AB + AC + BC >2AM
Hence, it is true.