## Geometry: Common Core (15th Edition)

$x = 28$
In similar triangles, corresponding sides are proportional to one another. Let us set up a proportion to find the relationship between two sides of one triangle and two sides of the other triangle: $\frac{30}{30 + 15} = \frac{84 - x}{84}$ Cross multiply to get rid of fractions: $(84 - x)(30 + 15) = 84(30)$ Evaluate what is in parentheses first: $(84 - x)(45) = 84(30)$ Multiply to simplify: $3780 - 45x = 2520$ Subtract $3780$ from each side of the equation to move constants to one side of the equation: $-45x = -1260$ Divide each side by $-45$ to solve for $x$: $x = 28$