ANSWER
The value of x is
[tex]9[/tex]
EXPLANATION
F is the point of intersection of the medians of the triangle,
The ratio is
[tex]IF:IZ=2:3[/tex]
This implies that,
[tex](2x + 2): (2x + 12) = 2: 3[/tex]
We can write this as a fraction to get,
[tex] \frac{2x + 2}{2x + 12} = \frac{2}{3} [/tex]
We cross multiply to get,
[tex]3(2x + 2) = 2(2x + 12)[/tex]
Let us expand the brackets yo obtain,
[tex]6x + 6 = 4x + 24[/tex]
We group like terms to get,
[tex]6x - 4x = 24 - 6[/tex]
[tex]2x = 18[/tex]
We divide both sides by 2 to get,
[tex]x = 9[/tex]
The correct answer is B.
