Question

If AM is a median of triangle ABC. Then AB +BC +CA $>$ 2AM

• A. AB+BC+CA = 2 AM
• B. AB+BC+CA > 2AM

Answer 1

The correct option is A

AB+BC+CA = 2 AM

Sum of lengths of any two sides of a triangle is always greater than the third side.
Hence, AB +BM $>$ AM;
AC +CM $>$ AM
Thus, AB +BC +CA $>$ 2AM

In $\Delta$ ABM

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

In $\Delta$ AMC

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

Adding (i) & (ii) we get

AB + BM + AC + CM > AM + AM

AB + AC + BC > 2AM