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