Answer
$x = 12$
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:
$\frac{x - 3}{x} = \frac{12}{16}$
Use the cross product property to get rid of the fractions:
$12x = 16(x - 3)$
Evaluate what is in parentheses first:
$12x = 16x - 48$
Subtract $16x$ from each side to move variables to one side of the equation:
$-4x = -48$
Divide each side of the equation by $-4$ to solve for $x$:
$x = 12$
