Points D, E and F are on the sides AB, BC and AC, respectively, of triangle ABC such that AE, BF and CD bisect ZA, ZB and 2C, respectively. If AB = 6 cm, BC = 7 cm and AC = 8 cm, then what will be the length of BE?
Show answer & explanation
Correct answer: D
Explanation
The correct answer is option 4 i.e. 3 cm.
Use angle bisector theorem for AE.
According to the theorem:
BE / EC = AB / AC
BE / EC = 6 / 8 = 3 / 4
Let BE = x.
Then EC = 7 - x.
So x / (7 - x) = 3 / 4
4x = 3(7 - x)
4x = 21 - 3x
7x = 21
x = 3