Inside a triangle ABC, a straight line parallel to BC intersects AB and AC at the points P and Q, respectively. If AB = 6PB, then PQ ∶ BC is _________.

5 : 6

It is given that , AB = 6PB

AB = AP + PB

AB - \(\frac{1}{6}\)AB = AP

AP = \(\frac{5}{6}\)AB

By using the concept :-

\(\frac{AP}{AB}\) = \(\frac{AQ}{AC}\) = \(\frac{PQ}{BC}\)

\(\frac{5AB}{6AB}\) = \(\frac{PQ}{BC}\)

\(\frac{5}{6}\) = \(\frac{PQ}{BC}\)

So, Ratio of PQ : BC = 5 : 6