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 is true because the perimeter of any triangle is indeed greater than the sum of the lengths of its medians. This is a well-established property in geometry, and it holds for all types of triangles. 
Statement II is also true. It is known as a triangle inequality for a point inside the triangle: if D is any point on side BC, then the sum of the distances from A to D, B to D, and C to D is always greater than the length of any side of the triangle. This inequality holds true for all triangles and is one of the fundamental results in geometry