Question

What is the value of x?

Enter your answer in the box.

x =
​​

Answer 1

The value of
`x` is 5.

Explanation:

Firstly, we'll name as P the point of intersection between the internal line of the triangle (that comes from the point A) with the side BC.

By the Angle Bisector Theorem, we can write the following relation

`(AB)/(BP)=(AC)/(PC)\\\\(9)/(2x-1)=(15)/(3x)\\\\(9)/(2x-1)=(5)/(x)\\\\9x = (2x-1)\cdot5\\\\9x = 10x - 5\\\\\boxed{x=5}`