XAT 2014 — QA & DI Question 10
Triangle ABC is a right angled triangle. D and E are mid points of AB and BC respectively. Read the following statements.
- AE = 19
- CD = 22
- Angle B is a right angle.
Which of the following statements would be sufficient to determine the length of AC?
Answer & solution
- A
Statement I and Statement II.
- B
Statement I and Statement III.
- C
Statement II and III.
- D
Statement III alone.
All three statements.
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).