XAT 2014 Question 59

Question 59

Triangle ABC is a right angled triangle. D and E are mid points of AB and BC respectively. Read
the following statements.
I. AE = 19
II. CD = 22
III. Angle B is a right angle.
Which of the following statements would be sufficient to determine the length of AC?

Solution

ABC is right angled triangle. D and E are mid points of AB and BC respectively.

As it is not given that which angle is 90°. So we need statement (III) to find the value of AC.

Whereas using statement (I) & (II) alone, we cannot find the value of AC.

But using all the three statements. We can find value of $$(AB)^2 + (BC)^2$$.

Hence, the value of $$AC = \sqrt{(AB)^2 + (BC)^2}$$ using Pythagoras Theorem.

=> Ans - (E) : All statements are required.



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