2023 · Q84
In a triangle ABC, angle B = 90° and p is the length of the perpendicular from B to AC. If BC = 10 cm and AC = 12 cm, then what is the value of p?
Elementary MathematicsGeometry: Lines, Angles and Triangles
- A5√11/3 cm
- B10√11/3 cm
- C40/√61 cm
- D12/25 cm
Explanation
In right △ABC with hypotenuse AC = 12 and BC = 10, the third side is AB = √(12² − 10²) = √44 = 2√11. The altitude p from the right angle to the hypotenuse satisfies p·AC = AB·BC (both equal twice the area), so p = (2√11 × 10)/12 = 20√11/12 = 5√11/3 cm. The answer is (A).