In the figure, AQ = 4√2 cm, QC = 6√2 cm and AB = 20 cm. If PQ is parallel to BC, then what is the value (in cm) of PB?
Show answer & explanation
Correct answer: B
Explanation
The correct answer is option 2 i.e. 12
PQ || BC
therefore, ∠APQ = ∠ABC (corresponding angles)
∠AQP = ∠ACB (corresponding angles)
∠PAQ = ∠BAC (common angles)
△APQ ~ △ABC
Let PB = 'a' cm
AP = (20 - a) cm
AP/AB = AQ/AC
⇒ (20 - A)/20 = 4√2/10√2 = 2/5
⇒ 100 - 5a = 40
⇒ a = 12 cm