Question

Which one of the following is a triangle?

• A. Sum of the medians is greater than the perimeter.
• B. Sum of the medians is less than the perimeter.
• C. Sum of the medians is equal to the perimeter.
• D. None of these.

Answer 1

Answer: (B)

Sum of the medians is less than the perimeter.

$AB+AC>2AR$
$AC+CD>2CP$
$CB+AB>2BQ$
From the above inequalities, we get
$2(AB+AC+BC)>2(AR+CP+BQ)$
or Perimeter > Sum of the medians