In the figure below, PQ || BC. If AP = 3, PB = 4 and AQ = 4, then QC =

1.	In the figure below, PQ \|\| BC. If AP = 3, PB = 4 and AQ = 4, then QC =(A) 7/3(B) 4/3(C) 16/3(D) 3/4
Answer» Correct option is (C) 16/3 \(\because\) PQ \|\| BC in \(\triangle ABC\) \(\therefore\) \(\triangle APQ\sim\triangle ABC\) \(\therefore\) \(\frac{AP}{AB}=\frac{AQ}{AC}\) \(\Rightarrow\) \(\frac{AP}{AB-AP}=\frac{AQ}{AC-AQ}\) \(\Rightarrow\) \(\frac{AP}{PB}=\frac{AQ}{QC}\) \(\Rightarrow\) \(QC=AQ.\frac{PB}{AP}\) \(=4.\frac43=\frac{16}3\) \((\because\) AQ = 4, PB = 4 & AP = 3 (given)) Correct option is: (C) \(\frac{16}{3}\)

In the figure below, PQ || BC. If AP = 3, PB = 4 and AQ = 4, then QC =(A) 7/3(B) 4/3(C) 16/3(D) 3/4

Answer»

Correct option is (C) 16/3

\(\because\) PQ || BC in \(\triangle ABC\)

\(\therefore\) \(\triangle APQ\sim\triangle ABC\)

\(\therefore\) \(\frac{AP}{AB}=\frac{AQ}{AC}\)

\(\Rightarrow\) \(\frac{AP}{AB-AP}=\frac{AQ}{AC-AQ}\)

\(\Rightarrow\) \(\frac{AP}{PB}=\frac{AQ}{QC}\)

\(\Rightarrow\) \(QC=AQ.\frac{PB}{AP}\)

\(=4.\frac43=\frac{16}3\) \((\because\) AQ = 4, PB = 4 & AP = 3 (given))

Correct option is: (C) \(\frac{16}{3}\)