Question

Given: Angle 1 = Angle 2. If AC:BC = 3:5 and AB = 12, find DB.

Answer 1

Answer:

C

Step-by-step explanation:

Angle's bisector property: Angle bisectors divide the opposite side in the ratio of the adjacent sides.

Let AD = x, then BD = 12 - x. Use the angle's bisector property:

$\dfrac{AC}{BC}=\dfrac{AD}{BD},\\ \\\dfrac{3}{5}=\dfrac{x}{12-x},\\ \\3(12-x)=5x,\\ \\36-3x=5x,\\ \\8x=36,\\ \\x=\dfrac{36}{8}=4.5.$

If AD=4.5, then BD=12-4.5=7.5.