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Prove that the perimeter of a triangle i...

Prove that the perimeter of a triangle is greater than the sum of its three medians.

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Let AD, BE and CF be the three medians of a `DeltaABC`.
We know that the sum of any two sides of a triangle is greater than twice the median drawn to the third side.

`therefore" "AB+ACgt2AD," ...(i)"`
`AB+BC gt 2BE" ...(ii)"`
and `BC+AC gt 2CF." ...(iii)"`
Adding, the corresponding sides of (i), (ii) and (iii), we get
`2(AB+BC+AC)gt 2(AD+BE+CF)`
`therefore" "(AB+BC+AC)gt(AD+BE+CF).`
Hence, the perimeter of a triangle is greater than the sum of its three medians.
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