Using the Angle Bisector Theorem solve for x.
The "Angle Bisector" Theorem says that an angle bisector of a triangle will divide the opposite side into two segments that are proportional to the other two sides of the triangle.
As, we see the figure, AD bisects angle A
So, Applying Angle Bisector theorem, we get,
[tex] \frac{AC}{CD} =\frac{AB}{BD} [/tex]
[tex] \frac{AC=15}{CD=3} =\frac{AB=(4x+1)}{BD=5} [/tex]
[tex] \frac{15}{3} =\frac{4x+1}{5} [/tex]
15 divide by 3 gives 5
So, we have
5=[tex] \frac{4x+1}{5} [/tex]
To get rid of fractions let us multiply by 5 on both sides
5*5=[tex] \frac{5*(4x+1)}{5} [/tex]
25=[tex] \frac{1*(4x+1)}{1} [/tex]
25=4x+1
To solve for x, let us subtract 1 from both sides
25-1=4x+1-1
24=4x+0
Or, 4x=24
To solve for x, let us divide by 4 on both sides
[tex] \frac{4}{4}x=\frac{24}{4} [/tex]
x=6
Answer: x=6
