PrepRung
Sign inSign up free

CAT 2022 Slot 3 · Quant · Triangles · medium

In right triangle ABC, angle A = 90°, AB = 9 and AC = 12. D is the foot of the perpendicular from A to BC. Find the length of AD.

Single correct option

In right triangle ABC, angle A = 90°, AB = 9 and AC = 12. D is the foot of the perpendicular from A to BC. Find the length of AD.
  1. A. 6
  2. B. 6.5
  3. C. 7.2
  4. D. 7.5
Show answer and solution

Answer: (C) 7.2

By Pythagoras, BC = √(9² + 12²) = √225 = 15. The altitude to the hypotenuse in a right triangle satisfies AD = (AB × AC)/BC (since area = ½·AB·AC = ½·BC·AD). AD = (9×12)/15 = 108/15 = 7.2.
Report a mistake

Original question written in the CAT 2022 Slot 3 pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake