Answer
$x = 5$
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:
$\frac{x}{10} = \frac{45 - 30}{30}$
Use the cross product property to get rid of the fractions:
$30x = 10(45 - 30)$
Evaluate what is in parentheses first:
$30x = 10(15)$
Multiply to simplify:
$30x = 150$
Divide each side of the equation by $30$ to solve for $x$:
$x = 5$
