Question

Given below are two statements : Statement I: The perimeter of a triangle is greater than the sum of its three medians. Statement II: In any triangle ABC, if D is any point on BC, then AB + BC + CA > 2 AD. In the light of the above statements, choose the correct answer from the options given below :

Accepted Answer

A. Statement I is true: The sum of the lengths of the medians of a triangle is always less than the perimeter. Statement II is true: In $	riangle ABD$, $AB + BD > AD$. In $	riangle ACD$, $AC + CD > AD$. Adding both inequalities gives $AB + AC + BC > 2AD$.

Triangle Medians and Inequality Statements

Explanation

Practise this under exam conditions