Question

In △ABC , AD is the angle bisector of ∠BAC . What is BD ?

Enter your answer, as a decimal, in the box.

in.

Answer 1

3.2 / 4 = BD / 3

BD = 3 * 3.2 / 4 = 2.4 (answer)

Answer 2

2.4 in

Explanation:

The triangle angle bisector theorem states that an angle bisector of an angle of a triangle divides the opposite side in two segments that are proportional to the other two sides of the triangle.

For this triangle, this gives us

CD/DB = AC/AB

3/x = 4/3.2

Cross multiplying,

3(3.2) = 4(x)

9.6 = 4x

Divide both sides by 4:

9.6/4 = 4x/4

2.4 = x