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CAT 2022 Slot 2 · Quant · Triangles · easy

In right triangle ABC, right-angled at A, AB = 9 cm and AC = 12 cm. D is the midpoint of the hypotenuse BC. Find the length of AD.

Single correct option

In right triangle ABC, right-angled at A, AB = 9 cm and AC = 12 cm. D is the midpoint of the hypotenuse BC. Find the length of AD.
  1. A. 6 cm
  2. B. 6.5 cm
  3. C. 7 cm
  4. D. 7.5 cm
Show answer and solution

Answer: (D) 7.5 cm

By Pythagoras, BC = √(9²+12²) = √(81+144) = √225 = 15 cm. The median to the hypotenuse of a right triangle equals half the hypotenuse (since D is equidistant from A, B and C, being the circumcenter of the right triangle). So AD = 15/2 = 7.5 cm.
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Original question written in the CAT 2022 Slot 2 pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake