In triangle ∆ABC, a straight line parallel to side BC intersects AB and AC at points P and Q respectively. Given that \(\frac{AQ}{QC} = \frac{3}{4}\) and AB = 21 cm, find the length of PB.

Q.In triangle ∆ABC, a straight line parallel to side BC intersects AB and AC at points P and Q respectively. Given that \(\frac{AQ}{QC} = \frac{3}{4}\) and AB = 21 cm, find the length of PB.

\(\because \frac{AQ}{QC} = \frac{3}{4}\) \(\therefore \frac{AQ}{QC} + 1 = \frac{3}{4} + 1\) i.e., \(\frac{AQ + QC}{QC} = \frac{3 + 4}{4}\) i.e., \(\frac{AC}{QC} = \frac{7}{4}\) Again, \(\frac{AB}{PB} = \frac{AC}{QC}\) i.e., \(\frac{21}{PB} = \frac{7}{4}\) i.e., \(7PB = 21 \times 4\) i.e., \(PB = 12\) \(\therefore\) The length of PB is 12 cm.