2022 · Q77
Consider the following statements :
- 1The sum of any two sides of a triangle is less than twice the median drawn to the third side.
- 2The perimeter of a triangle is greater than the sum of the three medians.
Which of the above statements is/are correct?
Elementary MathematicsGeometry: Lines, Angles and Triangles
- A1 only
- B2 only
- CBoth 1 and 2
- DNeither 1 nor 2
Explanation
Statement 1 reverses the true median inequality (b+c > 2m_a, proved by extending the median to form a parallelogram) - it is false. Statement 2, that the perimeter exceeds the sum of the three medians, is the standard median inequality - true. Hence the keyed option is B.