Question

Am is median of triangle abc prove that ab+bc+ac>2am

Answer 1

Hi friend ✋✋✋✋
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Your answer
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The median AM divides ∆ABC into two triangles , namely - ∆ABM and ∆AMC.

Now,
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In ∆ABM , we have,

AB + BM > AM [ Sum of any teri sides of a triangle is always greater than the third side] .....(i)

Similarly,
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In ∆ AMC , we gave,

MC + AC > AM [ Sum of any teri sides of a triangle is always greater than the third side] .....(ii)

Now, on adding equation (i) and (ii) , we get,

AB + BM + MC + AC > AM + AM

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

=> AB + BC + AC > 2AM [Because , BM + MC = BC]

HOPE IT HELPS