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AM is a median of a triangle ABC. Is AB + BC + CA > 2 AM? (Consider the sides of triangles ∆ABM and ∆AMC.)
Let us consider Δ ABM,
⇒ AB + BM > AM ….. [equation 1]
Now, consider the other triangle Δ ACM
⇒ AC + CM > AM … [equation 2]
By adding equation  and , we get,
AB + BM + AC + CM > AM + AM
From the figure we can observe that, BC = BM + CM
Therefore, AB + BC + AC > 2 AM
Hence, the given expression is true.
AM is a median of a triangle ABC. Is AB + BC + CA > 2 AM?
NCERT Solutions for Class 7 Maths Chapter 6 Exercise 6.4 Question 3
AM is a median of a triangle ABC. The given expression AB + BC + CA > 2 AM is true.
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