2018 · Q90
Consider the following for the next two (02) items:
In a triangle ABC, a, b and c are the lengths of the sides and p, q and r are the lengths of its medians.
Which one of the following is correct?
Elementary MathematicsGeometry: Lines, Angles and Triangles
- A(a + b + c) < (p + q + r)
- B3(a + b + c) < 4(p + q + r)
- C2(a + b + c) > 3(p + q + r)
- D3(a + b + c) > 4(p + q + r)
Explanation
The strict lower bound (3/4)(a + b + c) < p + q + r rearranges to 3(a + b + c) < 4(p + q + r), option (B). Option (A) reverses the known upper bound p + q + r < a + b + c, and (D) contradicts the lower bound.