Quantitative Aptitude Ques 342

Question: In $ \Delta ABC, $ X and Y are points on sides AB and BC respectively, such that $ XY||AC $ and XY divides triangular region ABC into two parts equal in area. Then, $ \frac{AX}{AB} $ is equal to

Options:

A) $ \frac{2+\sqrt{2}}{2} $

B) $ \frac{\sqrt{2}+3}{2} $

C) $ \frac{\sqrt{2}-1}{\sqrt{2}} $

D) $ \frac{3-\sqrt{2}}{2} $

Show Answer

Answer:

Correct Answer: C

Solution:

  • According to the question, $ \frac{Area,of,\Delta ABC}{Area,of,\Delta BXY}=\frac{2}{1} $

$ \Rightarrow $ $ \frac{AB}{BX}=\frac{\sqrt{2}}{1} $

$ \Rightarrow $ $ \frac{AB-BX}{BX}=\frac{\sqrt{2}-1}{1} $ $ \frac{AX}{BX}=\frac{\sqrt{2}-1}{1} $

$ \Rightarrow $ $ \frac{AX}{AX+BX}=\frac{\sqrt{2}-1}{\sqrt{2}-1+1} $

$ \Rightarrow $ $ \frac{AX}{AB}=\frac{\sqrt{2}-1}{\sqrt{2}} $

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