Answer
$x = 20$
Work Step by Step
With similar triangles, corresponding sides are proportional.
Let's set up a proportion using the two sets of corresponding sides that we are given:
$\frac{2x - 4}{24} = \frac{39}{x + 6}$
Cross multiply to get rid of the fractions:
$(2x - 4)(x + 6) = 24(39)$
Multiply the terms out:
$2x^2 - 4x + 12x - 24 = 936$
Combine like terms:
$2x^2 + 8x - 24 = 936$
Divide all terms by $2$:
$x^2 + 4x - 12 = 468$
Subtract $468$ from each side of the equation:
$x^2 + 4x - 480 = 0$
Factor the quadratic equation:
$(x + 24)(x - 20) = 0$
Set each factor equal to $0$ to solve for $x$:
$x + 24 = 0$
Subtract $24$ from each side of the equation to solve:
$x = -24$
We discard this solution because $x$ cannot be negative.
Let's look at the other factor:
$x - 20 = 0$
Add $20$ to each side of the equation:
$x = 20$
