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:

Answer: Option B

Solution

Answer: Option B

Solution:

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