M is point on side BC of a triagle ABC such that AM is the bisector of `angleBAC`.Is it ture to say that perimeter of the triangle is greater than 2 AM ? Give reason for your ancwer ?

Explanation

Yes ,in `Delta ABC,`,M is a point of side BC such that AM I the bisector of `angleBAC `
In `Delta ABM, " " AB+BM gt AM `
[Sum of two sides of a triangle is greater than the third side ]
`In Delta ACM, " " AC +CM + gt AM`
[Sum of two sides of a triangle is grater than the third side]

On adding Eqs.(i) and (ii) we get
`" " (AB+ BM+AC +CM)gt 2 AM`
`rArr (AB+BM+MC+AC)gt 2 AM`
`rArr " " AB +BC+ AC )gt 2 AM " "[because BC=BM+MC]`
` therefore" " "Perimeter of" Delta ABC gt 2 AM`