The value of x is [tex]5.625[/tex]
Explanation:
Since, from the figure we can see that, a ray bisects the angle of a triangle.
Then, the angle bisector theorem states that, "if a ray bisects an angle of a triangle, then it divides the opposite sides of the triangle into segments that are proportional to the other two sides".
Thus, we have,
[tex]$\frac{A C}{B C}=\frac{A D}{B D}$[/tex]
where [tex]AC=4, BC=7.5, AD=3[/tex] and [tex]DB=x[/tex]
Substituting the values, we get,
[tex]$\frac{4}{7.5}=\frac{3}{x}$[/tex]
Simplifying, we have,
[tex]4x=22.5[/tex]
Dividing both sides by 4,
[tex]x=5.625[/tex]
Thus, the value of x is [tex]5.625[/tex]
