Question

What is the value of x?

Answer 1

The value of x is $5.625$

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,

$\frac{A C}{B C}=\frac{A D}{B D}$

where $AC=4, BC=7.5, AD=3$ and $DB=x$

Substituting the values, we get,

$\frac{4}{7.5}=\frac{3}{x}$

Simplifying, we have,

$4x=22.5$

Dividing both sides by 4,

$x=5.625$

Thus, the value of x is $5.625$