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}} $
BETA
