Question

in the following figure , S is any point on side BC of triangle ABC . Prove that AB+BC+CA>2AS

Answer 1

$\textbf{ \huge{ Hello Mate! }}$

Given : S is any point on side BC of triangle ABC.

To Prove : AB + BC + CA > 2AS

Proof : By property of triangle that sum of two sides of triangle is greater than third side.

AB + BS > AS _____(1)

Similarily,

AC + CS > AS ____(2)

On adding (1) and (2)

AB + AC + ( BS + CS ) > AS + AS

AB + AC + BC > 2AS

$\textbf{ Q.E.D }$

Have great future ahead!