question_answer

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                                [SSC (CPO) 2013]

A) 4         

B) 2     

C) 1                                 

D) 8

Correct Answer: A

Solution :

Since, \[DE||BC\]

\[\therefore \]      \[\frac{AD}{DB}=\frac{AE}{EC}\]

[by basic proportionality theorem or Thales theorem]

\[\Rightarrow \]\[\frac{x}{x-2}=\frac{x+2}{x-1}\]

\[\Rightarrow \]\[{{x}^{2}}-x={{x}^{2}}-{{(2)}^{2}}\]

\[\Rightarrow \]\[{{x}^{2}}-x={{x}^{2}}-4\]

\[\Rightarrow \]\[-\,\,x=-\,\,4\]

\[\therefore \] \[x=4\]