Quantitative Aptitude Ques 1365
Question: In $ \Delta ABC, $ D and E are points on sides AB and AC, such that $ DE||BC. $ If $ AD=x, $ $ DB=x-2, $ $ AE=x+2, $ $ EC=x-1, $ then the value of x is
Options:
A) 4
B) 2
C) 1
D) 8
Show Answer
Answer:
Correct Answer: A
Solution:
- Since, $ DE||BC $
$ \therefore $ $ \frac{AD}{DB}=\frac{AE}{EC} $ [by basic proportionality theorem or Thales theorem]
$ \Rightarrow $ $ \frac{x}{x-2}=\frac{x+2}{x-1} $
$ \Rightarrow $ $ x^{2}-x=x^{2}-{{(2)}^{2}} $
$ \Rightarrow $ $ x^{2}-x=x^{2}-4 $
$ \Rightarrow $ $ -x=-4 $
$ \therefore $ $ x=4 $
BETA
