## Algebra 1

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 $7-4=3$