2025 · Q57
Consider the following for the next two (02) items that follow: The perimeter of a triangle ABC is 105 cm. The altitudes AD, BE and CF are in the ratio 3 : 5 : 6. What is AB : BC : CA equal to?
Elementary MathematicsGeometry: Lines, Angles and Triangles
- A10 : 6 : 5
- B5 : 10 : 6
- C6 : 5 : 3
- D3 : 5 : 6
Explanation
Equal areas give (1/2)a·3x = (1/2)b·5x = (1/2)c·6x, so 3a = 5b = 6c and a:b:c = 10:6:5. With AB = c, BC = a, CA = b, the ratio AB:BC:CA = 5:10:6, option (b).