In a triangle ABC, Point P and Q are on AB and AC, respectively, such that AP = 4cm, PB = 6cm, AQ = 5cm and QC = 7.5cm. If PQ = 6cm, then find BC (in cm).
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e. 15
In triangle ABC and triangle APQ,
AP/AB = 4/10 = 2/5
AQ/AC = 5/12.5 = 2/5
So, AB/AP = AC/AQ
So, triangle ABC ~ triangle APQ,
So, PQ/BC = 2/5
⇒ 6/BC = 2/5
⇒ BC = 6 × (2/5) = 15