Question

AD is median of triangle ABC is it true that AB+AC+BC>2AD

Answer 1

Here's your answer!!

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It's given that,

AD is the median of the ∆ABC,

It means, BD=CD
Because the median divides the line into two equal parts.

So,

<BAD =<CAD ( as AD is median and bisecting <BAC at A)

We know that,

In triangle Sum of two sides is Always greater than the third one.

So,

=> AB + BD > AD......(i)

And,

=>AC +CA > AD ......(ii)

Adding equation (i) and (ii), we get :-

=>AB +BD +AC+CA >2AD

=>AB + BC + CA > 2AD ( Since, BD +AC =AC )

Hence, Proved

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Hope it helps you!! :)