-
If AD, BE and CF are medians of ∆ ABC, then which one of the following statements is correct ?
-
- (AD + BE + CF) < AB + BC + CA
- AD+BE + CF > AB + BC + CA
- AD+BE + CF = AB + BC + CA
- AD+BE+CF= √2(AB+BC+ CA)
- (AD + BE + CF) < AB + BC + CA
Correct Option: A
Firstly , We draw a figure of triangle ABC whose AD, BE and CF are medians , 
Points D, E, F are midpoints of BC, CA and AB respectively.
Any two sides of a triangle are together greater than twice the median drawn to the third side.
∴ AB + AC > 2AD
AB + BC > 2BE
BC + CA > 2CF
On adding, we get
2 (AB + BC + CA) > 2 (AD + BE + CF)
∴ AB + BC + CA > AD + BE + CF
