In ∆ ABC, DE ‖ AB, where D and E are points on sides AC and BC, respectively. F is a point between C and D such that EF ‖ BD. If AD = 15 cm, DC = 10 cm, then the length of CF is:
Show answer & explanation
Correct answer: D
Explanation
The correct answer is Option 4 i.e. 4 cm.
In ∆ ACB & In ∆ DCE (DE ‖ AB)
CD/DA = CE/EB = 10/15 = 2/3
Now , In ∆ FCE & ∆ DCB (EF ‖ BD)
FC/DC = EC/BC = EC/(EC + EB) = 2/5
FC/DC = 2/5
FC = 2(10/5) = 4 cm