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:

• A. Both Statement I and Statement II are true
• B. Both Statement I and Statement II are false
• C. Statement I is true but Statement II is false
• D. Statement I is false but Statement II is true

Answer 1

The Correct Option is A

Statement I: True. The perimeter of any triangle exceeds the sum of its medians. This is a fundamental geometric property applicable to all triangle types.
Statement II: Also true. This is a triangle inequality for a point within the triangle. If D is on side BC, the sum of distances AD, BD, and CD always surpasses the length of any triangle side. This inequality applies universally and is a core geometric result.