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

Solution:

We know that, the sum of the length of any two sides is always greater than the third side. 

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 [1] and [2], 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.

☛ Check: NCERT Solutions Class 7 Maths Chapter 6

Video Solution:

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

Summary:

AM is a median of a triangle ABC. The given expression AB + BC + CA > 2 AM is true.

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