2026 · Q56
ABC is a triangle right-angled at B. Points M and N trisect BC. If AM = 6 cm and AN = 9 cm, then what is AC equal to?
Elementary MathematicsGeometry: Lines, Angles and Triangles
- A4√39 cm
- B2√39 cm
- C24 cm
- D20 cm
Explanation
Let BM=MN=NC=t, so BC=3t. Then AB²+t²=36 (from AM) and AB²+4t²=81 (from AN). Subtracting: 3t²=45, so t²=15 and AB²=21. Then AC²=AB²+9t²=21+135=156, giving AC=2√39 cm, option B.