Answer
$x = 5.2$
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:
$\frac{x}{13 - x} = \frac{2}{3}$
Use the cross product property to get rid of the fractions:
$2(13 - x) = 3x$
Use the distributive property first:
$26 - 2x = 3x$
Add $3x$ to both sides of the equation to move variables to one side of the equation:
$5x = 26$
Divide each side of the equation by $5$ to solve for $x$:
$x = 5.2$
