Question

ABC is a triangle, PQ is line segment intersecting AB in P and AC in Q and PQ II BC. The ratio of AP : BP = 3 : 5 and length of BC is 48 cm. The length of PQ is:

• A. 18 cm
• B. 28 cm
• C. 48 cm
• D. 39 cm

Answer 1

Answer:

A. 18 cm

Solution:

Given:

PQ II BC.

The ratio of AP : BP = 3 : 5

Length of BC is 48 cm

AP ∶ BP = 3 ∶ 5 

AB = 3 + 5

⇒ 8 units

Here,

∠A is common in ΔAPQ and ΔABC

PQ II BC

So,

ΔAPQ ∼ ΔABC

AP/AB = PQ/BC

⇒ 3/8 = PQ/48

⇒ PQ = 48 × 3/8 

⇒ PQ = 18 cm

∴ The length of PQ is 18 cm.