In ABE, D and C are the points on sides AE and EB, respectively, such that DC II AB. If AD = 4 cm, BC = 5 cm, DC = 10 cm, and AB = 15 cm, then the sum of the lengths of DE and EC is:
Show answer & explanation
Correct answer: D
Explanation
The correct answer is Option 4 i.e. 18 cm.
DC || AB and ΔEDC ~ ΔEAB
DE/EA = EC/EB = DC/AB
⇒ DE/(DE + AD) = EC/(EC + CB) = 10/15 = 2/3
DE/(DE + 4) = 2/3
⇒ DE = 8 cm
Also, EC/(EC + 5) = 2/3
⇒ EC = 10
Now, DE + EC = 10 + 8 = 18 cm