Answer
$x = 10$
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:
$\frac{x + 5}{x} = \frac{12}{8}$
Use the cross product property to get rid of the fractions:
$8(x + 5) = 12x$
Use the distributive property first:
$8x + 40 = 12x$
Subtract $8x$ from both sides of the equation to move variables to one side of the equation:
$4x = 40$
Divide each side of the equation by $4$ to solve for $x$:
$x = 10$
