In △ABC, D is the mid - point od sides AC and E is a Point on side AB such that EC bisects BD at F. If AE = 30 cm , then the length of EB is :
Show answer & explanation
Correct answer: D
Explanation
The correct answer is option 4 i.e. 15 cm
Given :
In △ABC, D is the mid - point on sides AC and E is a Point on side AB
EC bisects BD at F
AE = 30 cm
Calculations :
In the figure above a line is drawn parallel to EC from point D on side AE at G.
In ΔAEC, DG || EC
⇒ AG/GE = AD/DC
⇒ AG = GE and AD = DC
Similarly in ΔBGD, GD || EF
⇒ EB/EG = BF/FD
⇒ EB = GE and BF = FD
⇒ AE = AG + GE = 30
⇒ AG = GE = 15 cm
⇒ GE = EB = 15 cm
Hence, The value of EB is 15 cm