In triangle ABC, D and E are the points on sides AB and BC respectively such that DE || AC. If AD : DB = 5 : 3, then what is the ratio of the area of triangle BDE to that of the trapezium ACED?
Show answer & explanation
Correct answer: B
Explanation
The correct answer is option 2 i.e. 9 : 55.
Ar (BDE) : Ar (ABC) = (BD)² : (AB)²
⇒ (3)² : (8)²
⇒ 9 : 64
Hence,
Ar (BDE) : Ar (ADEC)
⇒ 9 : [Ar(ABC) - Ar(BDE)]
⇒ 9 : (64 - 9)
⇒ 9 : 55