Answer
B
Work Step by Step
The area of a triangle is $\frac{1}{2}bh$. Substitute the given values and solve for x to find the height.
$24=\frac{1}{2}(2x+2)(x-4)\longrightarrow$ multiply each side by 2
$24\times2=\frac{1}{2}(2x+2)(x-4)\times2\longrightarrow$ multiply
$48=(2x+2)(x-4)\longrightarrow$ multiply the binomials using the FOIL method
$48=2x^2-8x+2x-8\longrightarrow$ subtract 48 from each side
$48-48= 2x^2-8x+2x-8-48\longrightarrow$ combine like terms
$0=2x^2-6x-56$ factor the trinomial
$0=(2x-14)(x+4)$ one of the binomials must equal 0
$2x-14=0$ or $x+4=0$
$2x=14$ or $x=-4$
$x=7$ or $x=-4$
The height is x-4. Since the height cannot be negtive, x is 7.
The height is $7-4=3$
