2022 · Q76
Triangle ABC is right-angled at A and AD is perpendicular to BC. If BD = 7.5 cm and DC = 10 cm, then what is AD equal to?
Elementary MathematicsGeometry: Lines, Angles and Triangles
- A5 cm
- B5√2 cm
- C5√3 cm
- D10 cm
Explanation
In a right triangle the altitude to the hypotenuse satisfies AD² = BD·DC = 7.5×10 = 75, so AD = 5√3 cm. The geometric-mean relation AD² = BD·DC is the right-triangle altitude theorem. The keyed option is C.