Question

The perimeter of a triangle is.... the sum of its medians.

• A. Greater Than Twice
• B. Less Than
• C. Equal To
• D. Greater Than

Answer 1

The correct option is D

Greater Than

Let ABC be the triangle and AD, BE and CF be the medians as shown in the figure.

Sum of any two sides of a triangle is greater than twice the median bisecting the third side.

AB + AC > 2 AD, AB +BC > 2 BE and BC + AC > 2 CF

Adding the above you get

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

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