Answer : The value of x is 5.
Step-by-step explanation :
According to the angle bisector theorem, 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.
That means,
[tex]\frac{AB}{BD}=\frac{AC}{CD}[/tex]
[tex]\frac{9}{2x-1}=\frac{15}{3x}[/tex]
By the cross multiplication, we get:
[tex]9\times 3x=(2x-1)\times 15[/tex]
[tex]27x=30x-15[/tex]
[tex]30x-27x=15[/tex]
[tex]3x=15[/tex]
[tex]x=\frac{15}{3}[/tex]
[tex]x=5[/tex]
Therefore, the value of x is 5.
