# 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 other triangle which is 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.

**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

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

The given expression AB + BC + CA > 2 AM is true