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] |
\[\Rightarrow \]\[\frac{x}{x-2}=\frac{x+2}{x-1}\] |
\[\Rightarrow \]\[{{x}^{2}}-x={{x}^{2}}-{{(2)}^{2}}\] |
\[\Rightarrow \]\[{{x}^{2}}-x={{x}^{2}}-4\] |
\[\Rightarrow \]\[-\,\,x=-\,\,4\] |
\[\therefore \] \[x=4\] |
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