2018 · Q89
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
- A2(p + q + r) = (a + b + c)
- B2(p + q + r) > 3(a + b + c)
- C2(p + q + r) < 3(a + b + c)
- D11(p + q + r) > 10(a + b + c)
Explanation
For any triangle, (3/4)(a + b + c) < p + q + r < a + b + c. Only option (C), 2(p + q + r) < 3(a + b + c), is guaranteed by this; option (D) fails for nearly degenerate (flat) triangles, option (B) would need the sum to exceed 1.5 perimeters, and (A) is an equality that never holds. The keyed answer is (C).