2021 · Q85
Consider the following for the next two (02) items that follow : ABC is triangle in which AB = AC and D is any point on BC. If AD = 5 cm, BD = 4 cm and CD = 6 cm, then what is AB equal to ?
Elementary MathematicsGeometry: Lines, Angles and Triangles
- A7 cm
- B6.5 cm
- C6 cm
- D5.5 cm
Explanation
For a triangle with AB = AC and D on BC, the relevant relation (a consequence of Stewart's theorem, proved as Q84) is AB² = AD² + BD × CD. Substituting AD = 5, BD = 4, CD = 6: AB² = 25 + 4 × 6 = 25 + 24 = 49. Taking the positive root, AB = 7 cm. The 4 cm and 6 cm segments combine multiplicatively, not additively — adding them would give the wrong √51. Hence option (A) 7 cm.