Question 59

# Triangle ABC is a right angled triangle. D and E are mid points of AB and BC respectively. Readthe following statements.I. AE = 19II. CD = 22III. 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.