In a ∆ABC, a line DE is drawn from D point on AB to E point on AC such that DE is parallel to BC. Also AD : DB is 2 : 5. If AC is 4.2 cm, then what is the length of AE?
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e. 1.2 cm
DE is parallel to BC and D and E are the midpoints of AB and AC respectively, we have
AD = DB and AE = EC
We have AD/DB = 2/5 and AC = 4.2 cm
So, according to the midpoint theorem,
⇒AD / (AD + DB) = AE / (AE + EC) = AD / AB = AE / AC
⇒2/7 = AE/4.2
⇒AE = 2/7 × 4.2 = 1.2