Answer
$x = 77$
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:
$\frac{x}{55} = \frac{63}{45}$
Use the cross product property to get rid of the fractions:
$45x = 3465$
Divide each side of the equation by $45$ to solve for $x$:
$x = 77$
