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 _________.
Answer & explanation
Correct answer: option 4
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