Question

In a ΔABC , AD is the bisector of ∠BAC. If AB = 6 cm, AC = 5 cm and BD = 3 cm„ then DC =
A. 11.3 cm
B. 2.5 cm
C. 3 5 cm
D. None of these.

Answer 1

B. 2.5 cm

Step-by-step explanation:

Given:

In a ΔABC , AD is the bisector of ∠BAC.  

AB = 6 cm, AC = 5 cm and BD = 3 cm.

According to the angle bisector theorem, an angle bisector of a triangle will divide its opposite side into two segments that are proportional to the other two sides of the triangle.

So AB/AC = BD/DC

6/5 = 3/DC

DC = 3 * 5 / 6 = 2.5cm.

Option B is the answer.