2024 · Q57
Consider the following for the next two items that follow: ABC is a triangle right-angled at B. Given that AC − AB = 2 cm and BC = 16 cm. If BD is the perpendicular on the side AC, then what is the length of BD?
Elementary MathematicsGeometry: Lines, Angles and Triangles
- A1008/65 cm
- B756/65 cm
- C168/7 cm
- D165/7 cm
Explanation
From Q56 the legs are 63 cm and 16 cm with hypotenuse 65 cm. The altitude from the right angle to the hypotenuse equals (product of legs)/(hypotenuse) — equivalently 2×Area/AC. This gives BD = (63×16)/65 = 1008/65 cm — option A.