Can someone me out with this geometry problem? i've been stuck on it for almost an hour.

The answer is

Step-by-step explanation:

Solution:

Let we first name the Triangle as Δ ABC and ray BD as a bisector of ∠B

as shown in the figure below.

As ray BD is the bisector of angle B so, by Angle bisector theorem property we have

∴

∴

∴

∴    final answer

25/4

step-by-step explanation:

call segment cd's length x. because dc and ab are parallel, angle acd and cab, so triangles adc and abc are similar and we can set up the equation x / ac = ac / ab, or x / 5 = 5 / 4 and x = 25/4.