Answer
$x = 8$
Work Step by Step
According to the side-splitter theorem, if a line is parallel to a side of a triangle and intersects the other two sides, then those two sides are divided proportionately.
Let's set up a proportion for the sides whose values are given in the figure:
$\frac{x + 4}{2x} = \frac{9}{12}$
Use the cross product property to get rid of the fractions:
$12(x + 4) = 18x$
Use the distributive property first:
$12x + 48 = 18x$
Subtract $12x$ from both sides of the equation to move variables to one side of the equation:
$6x = 48$
Divide each side of the equation by $6$ to solve for $x$:
$x = 8$
