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XAT 2014 — QA & DI Question 10

Simple EquationsEasy

Triangle ABC is a right angled triangle. D and E are mid points of AB and BC respectively. Read the following statements.

  1. AE = 19
  2. CD = 22
  3. Angle B is a right angle.

Which of the following statements would be sufficient to determine the length of AC?

Answer & solution

Correct answer: All three statements.

  • A

    Statement I and Statement II.

  • B

    Statement I and Statement III.

  • C

    Statement II and III.

  • D

    Statement III alone.

  • All three statements.

Solution

Option 1: If we take statements I and II, we have 2 medians of a right angled triangle, without knowing which angle is a right angle.

Option 2: If we take statements I and III, we have 1 median of a right angled triangle, and B is the right angle.

Option 3: If we take only statements II and III, we have 1 medians of a right angled triangle, and B is the right angle.

Option 4: If we only know that B is a right angle, we cannot determine the length of AC.

Option 5: If we have all 3 statements, then we have 2 medians of a right angled triangle, and we know B is the right angle. Hence, we can find AC.

Hence, option (e).

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XAT 2014 QA & DI Q10: Triangle ABC is a right angled triangle. D and E are mid points of AB and BC respectively. Read the following — Solution | TheCATExam