question_answer

In\[\Delta ABC\], the straight line parallel to the side BC meets AB and AC at the points P and Q respectively. If AP = QC the length of AB is 12 units and the length of AQ is 2 units, then the length (in units) of CQ is

A)  4                    

B)  6

C)  8                    

D)  10

Correct Answer: A

Solution :

 \[\therefore \] PQ\[ll\]BC \[\Rightarrow \,\,\,\,\frac{AP}{AB}=\frac{AQ}{AC}\Rightarrow \frac{AP}{AQ}=\frac{AB}{AQ}\] \[\Rightarrow \,\,\,\,\frac{AP}{2}=\frac{12}{AC}\Rightarrow \,\,\,AC\,\,.\,\,AP=24\] \[\Rightarrow \] (AQ + QC). QC = 24 \[\Rightarrow \] (2 +QC). QC = 24 \[\Rightarrow \]QC\[^{2}\]+ 2QC ? 24 = 0 \[\Rightarrow \](QC + 6) (QC - 4) = 0 \[\Rightarrow \]QC = \[\]