question_answer

In \[\Delta ABC,\]\[DE\parallel BC,\]where DE intersects AB and AC at the points D and E respectively. If \[AD=6\,cm,\]cm,\[DB=12x-6\,cm,\]\[AE=2x\,cm\]and\[CE=16-2x\text{ }cm,\] then the value of x is

A) 6 cm

B) 4 cm

C) 2 cm

D) 8 cm

Correct Answer: C

Solution :

[c] Given, DE || BC \[\therefore \]      \[\Delta ADE\sim \Delta ABC\] Then, \[\frac{AB}{AD}=\frac{AC}{AE}\]\[\Rightarrow \]\[\frac{12x}{6}=\frac{16}{2x}\] \[\Rightarrow \]   \[{{x}^{2}}=\frac{16\times 16}{12\times 2}=4\]\[\Rightarrow \] x = 2 cm