AD is a median of the `Delta ABC`.Is it trure `AB+BC+CA gt 2 AD `? Give reason for your answer

Explanation

Yes

In `Delta ABD, we have " " AB+BD gt AD`
`" " ` [Sum of any two sides of a triangle is great than third side]
In `Delta ACD,We have " " AC + CD gt AD`
[Sum of any two sides of a triangle is greater than third side]
On adding Eqs.(i) and (ii) we get
` (AB +BD +CD + AC)gt 2AD `
`rArr " " (AB + BD +CD + AC ) gt 2 AD `
`Hence " " AB+ BC +AC gt 2 AD " " [because BC = BD +CD]`