Question

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

• A. Greater
• B. Lesser
• C. Equal
• D. May be greater or lesser

Answer 1

The correct option is A Greater

Given: $△ABC$, AD, BE and CF are medians from A, B and C respectively on the corresponding sides.
We know that sum of any two sides of the triangle is greater than twice the median bisecting the third side
Hence, $AB+AC>2AD$ (1)
$AB+BC>2BE$ (2)
$BC+AC>2CF$ (3)
Adding the three equations:
$2(AB+BC+AC)>2(AD+BE+CF)$
$AB+BC+AC>AD+BE+CF$
Hence, the perimeter of the triangle is greater than the sum of the medians.