GMAT Quantitative Reasoning Practice Test 1

Since we are trying to find the width of the deck, let $\mathit{x}=$ the width of the deck. Therefore, $\mathit{x}+\mathit{x}+20$ or $2\mathit{x}+20$ is the width of the entire figure. In the same way, $\mathit{x}+\mathit{x}+28$ or $2\mathit{x}+28$ is the length of the entire figure.
The area of a rectangle is length $\mathrm{times}$ width, so use $\mathit{A}=\mathit{l}\mathrm{times}\mathit{w}$. Substitute into the equation: $884=\left(2\mathit{x}+20\right)\left(2\mathit{x}+28\right)$
Multiply using FOIL: $884=4{\mathit{x}}^2+56\mathit{x}+40\mathit{x}+560$
Combine like terms: $884=4{\mathit{x}}^2+96\mathit{x}+560$
Subtract 884 from both sides: $884-884=4{\mathit{x}}^2+96\mathit{x}+560-884$
$0=4{\mathit{x}}^2+96\mathit{x}-324$
Divide each term by 4: $0={\mathit{x}}^2+24\mathit{x}-81$
Factor the trinomial: $0=\left(\mathit{x}+27\right)\left(\mathit{x}-3\right)$
Set each factor equal to zero and solve: $\mathit{x}+27=0$ or $\mathit{x}-3=0\mathit{x}$ $=-27\mathit{x}=3$
Since we are solving for a length, the solution of -27 must be rejected. The width of the deck is 3 feet.