Question

M is a point on side BC of a tri.ABC such that AM is the bisector of /_BAC.Is it true to say that perimeter of the triangle is greater than 2AM? Give reason for your answer.​

Answer 1

Step-by-step explanation:

As long as point MM is on line BC,BC, the perimeter of △ABC△ABC would be greater than 2AM.2AM.

The sum of the two sides of a triangle is always greater that the third side.

In △ABM

AB+BM>AM ......(1)

In △ACM,

AC+CM>AM ......(2)

Now, adding equation (1) and (2),

AB+BM+AC+CM>AM+AM

AB+AC+BC>2AM

Hence, the perimeter of △ABC is greater than 2AM.