Question

AM is Median of triangle ABC. Is AB+BC+CA>2AM

(consider the sides of triangle ∆ABM & ∆AMC)​

Answer 1

Answer:

We know,

In a triangle sum of two sides is greater than the third side

Hence,In triangle ABM 

AB + BM > AM  .........1

Also in triangle ACM

AC + MC > AM ..........2

Adding equation 1 and 2 we get,

AB + BM + AC + MC  > AM + AM

AB + AC + (BM + MC) > 2AM

AB + AC + BC > 2AM

Answer 2

Explanation:

we know that sum of two side is greater then the third side .

SO, in triangle ABM

AB+BM>AM................(i)

in triangle ACM

AC+MC>AM...............(ii)

adding equation (i) and (ii)

AB+BM+AC+MC>AM+AM

(from fig)

AB +(BM +MC)+ AC> AM +AM

AB +BC+ AC >2AM........hence proved............

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