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Question
In the given figure, AM is a median of Δ ABC.
Is AB + BC + CA > 2AM?
Is AB + BC + CA > 2AM?
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Solution
Since, the sum of lengths of any two sides in a triangle should be greater than the length of third side.
Therefore, In Δ ABM, AB + BM > AM ……….(i)
In Δ AMC, AC + MC > AM ……….(ii)
Adding eq. (i) and(ii),
AB + BM + AC + MC > AM +AM
⇒ AB + AC + (BM + MC) >2AM
⇒ AB + AC + BC >2AM
Hence, it is true.
Therefore, In Δ ABM, AB + BM > AM ……….(i)
In Δ AMC, AC + MC > AM ……….(ii)
Adding eq. (i) and(ii),
AB + BM + AC + MC > AM +AM
⇒ AB + AC + (BM + MC) >2AM
⇒ AB + AC + BC >2AM
Hence, it is true.
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