Question

Need quick help please?! Using the Angle Bisector Theorem solve for x. Show all work.

Answer 1

From the angle bisector theorem;
 15/3= (4x+1)/5
solving for x;
4x+1 = 25
     4x= 24
       x= 6

Answer 2

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,

$\frac{AC}{CD} =\frac{AB}{BD}$

$\frac{AC=15}{CD=3} =\frac{AB=(4x+1)}{BD=5}$

$\frac{15}{3} =\frac{4x+1}{5}$

15 divide by 3 gives 5

So, we have

5=$\frac{4x+1}{5}$

To get rid of fractions let us multiply by 5 on both sides

5*5=$\frac{5*(4x+1)}{5}$

25=$\frac{1*(4x+1)}{1}$

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

$\frac{4}{4}x=\frac{24}{4}$

x=6

Answer: x=6