Question

Prove that in a triangle four times the sum of its medium is greater than thrice its perimeter

Answer 1

Answer:

Your question is -

Prove that in a triangle four times the sum of its median is greater than thrice its perimeter

AD, CF and BE are median of ∆ABC.

Now, we know that, sum of two sides of a triangle is greater than twice its median.

So,

AB+AC > 2AD _____(i)

SIMILARLY,

BC+AB > 2BE ______(ii)

AND BC+AC > 2CF _______(iii)

Now, add (i), (ii) and(iii)

AB + AC +BC+AB+BC+AC > 2(AD+BE+CF)

2(AB+BC+AC) > 2(AD+BE+CF)