Question

What is the value of x?

Enter your answer, as a decimal, in the box. Do not round your answer.
x=

Answer 1

The value of x is
`5.625`

Step-by-step 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,

`$(A C)/(B C)=(A D)/(B D)$`

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

Substituting the values, we get,

`$(4)/(7.5)=(3)/(x)$`

Simplifying, we have,

`4x=22.5`

Dividing both sides by 4,

`x=5.625`

Thus, the value of x is
`5.625`