## Geometry: Common Core (15th Edition)

$x = 12$
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 $x$: $x = 12$