ABC is a triangle, PQ is line segment intersecting AB is P and AC in Q and PQ || BC. The ratio of AP : BP = 3 : 5 and length of PQ is 18 cm. The length of BC is:

Solution (By Examveda Team)

∵ PQ || BC
So ∠AQP = ∠ACB = α
and
∠APQ = ∠ABC = β
So, ΔABC and ΔAPQ
$$\eqalign{ & \frac{{AP}}{{AB}} = \frac{{PQ}}{{BC}} \cr & \frac{3}{8} = \frac{{PQ}}{{BC}} \cr & \frac{3}{8} = \frac{{18}}{{BC}} \cr & BC = 48\,{\text{cm}} \cr} $$