## Geometry: Common Core (15th Edition)

$x = 20$
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 $x$: $x = 20$