question_answer

If in\[\Delta ABC,\] \[AB=6cm\] and \[DE\left\| BC \right.\] such that \[AE=\frac{1}{4}AC,\]then the length of AD is:

A) \[2\,cm\]

B) \[1.2\,cm\]

C) \[1.5\,cm\]

D) \[4\,cm\]

Correct Answer: C

Solution :

[c] In \[\Delta ABC,\] \[DE||BC\]

\[\therefore \,\,\,\,\,\,\frac{AB}{AD}=\frac{AC}{AE}\]      (By Thales theorem)

\[\Rightarrow \,\,\,\,\,\,\,\,\,\,\,\frac{6}{AD}=\frac{AC}{\frac{1}{4}AC}\,\,\,\,\,\,\,\,\left[ AE=\frac{1}{4}AC\,\,(given) \right]\]

\[\Rightarrow \,\,\,\,\,\,\,\,\,\,\,AD=\frac{6}{4}=1.5\,\,cm\]