2022 · Q12
The perpendicular dropped from a vertex of the right-angled triangle upon the hypotenuse divides it into two segments of lengths 9 units and 16 units respectively. What is the length of the perpendicular?
Elementary MathematicsGeometry: Lines, Angles and Triangles
- A6 units
- B8 units
- C10 units
- D12 units
Explanation
By the right-triangle altitude theorem, the altitude to the hypotenuse is the geometric mean of the two segments: h² = 9x16 = 144, so h = 12 units. Hence the keyed option is D.