Answer
$x = 28$
Work Step by Step
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 $x$:
$x = 28$
