Answer
$x = 20$
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. If the ratios are equal to one another, then we can conclude that the red segments are parallel:
$\frac{12}{30} = \frac{x}{2x + 10}$
Use the cross product property to get rid of the fractions:
$30x = 12(2x + 10)$
Use the distributive property first:
$30x = 24x + 120$
Subtract $24x$ from each side of the equation to move variables to the left side of the equation:
$6x = 120$
Divide each side of the equation by $6$ to solve for $x$:
$x = 20$
