Question

Prove that the sum of the three sides of a triangle is greater than the sum of its three medians

Answer 1

◆Ekansh Nimbalkar◆
Hello friend here is your required answer

Answer 2

Given -- ABC is a triangle with medians AD, BE and CF on sides on BC,CA and AB respectively.

To prove - AB + BC + AC > AD + BE + CF

Proof -- We know that sum of 2 sides of a triangle is greater than 2 times the median bisecting the 3rd side of that triangle.

So,
 AB + AC > 2AD ------(i)
BC + AC > 2CF -------(ii)
BC + AB > 2BE -------(iii)

Adding (i) , (ii) and (iii)
2 ( AB + BC + CA) > 2 ( AD + BE + CF)

Cancelling out '2',
AB + BC + CA > AD + BE + CF

Hence Proved!

Hope This Helps You!