Consider the following statements :<br>1. The sum of any two sides of a triangle is less than twice the median drawn to the third side.<br>2. The perimeter of a triangle is greater than the sum of the three medians.<br>Which of the above statements is/are correct?
- A. 1 only
- B. 2 only ✓
- C. Both 1 and 2
- D. Neither 1 nor 2
Correct Answer: B. 2 only
Explanation
Statement 1 is false: The sum of any two sides is strictly greater than twice the median drawn to the third side (AB+AC \gt 2AD). Statement 2 is true: Summing the inequalities AB+AC \gt 2AD, BC+BA \gt 2BE, and CA+CB \gt 2CF gives 2(AB+BC+CA) \gt 2(AD+BE+CF), meaning Perimeter \gt Sum of medians.
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