Given:
In triangle ABC, AE is the angle bisector.
[tex]AB=4, BE=2, AC=x, CE=3[/tex]
To find:
The value of x.
Solution:
According to the angle bisector theorem, the angle bisector of a triangle divides the opposite side of the triangle into two parts. These two parts are proportional to the other two sides of the triangle.
Using the angle bisector theorem, we get
[tex]\dfrac{AB}{AC}=\dfrac{BE}{CE}[/tex]
[tex]\dfrac{4}{x}=\dfrac{2}{3}[/tex]
On cross multiplication, we get
[tex]4\times 3=2\times x[/tex]
[tex]12=2x[/tex]
Divide both sides by 2.
[tex]\dfrac{12}{2}=x[/tex]
[tex]6=x[/tex]
Therefore, the value of x is 6.
