Xavier Aptitude Test 2014 Paper

Question : 57 of 103

Marks: +1, -0

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 ?

Statement I and Statement II.
Statement I and Statement III.
Statement II and III.
Statement III alone.
All three statements.

Validate

Solution:

(e) Using AE = 19, CD = 22, ∠B = 90°, we can find thelength of AC.

\ {AB}^{2}+ (\ {\ {BC}}/{2} )^{2}=(19)^{2}

........(i)

\ (\ {\ {AB}}/{2}\ )^{2}+\ {BC}^{2}=(22)^{2}

.......(ii)
On adding (i) and (ii),

⇒A B^{2}+B C^{2}=\ {4}/{5}(361+484)

⇒ A C^{2}=676

\⇒A C=26

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