Answer
The possible dimensions of the rectangle are $n+4$ and $n-7$.
Work Step by Step
To factor $n^{2}-3n-28$, identify the pair of factors of $-28$ that has a sum of $-3$.
$\left[\begin{array}{lll}
\text{Factors of -28 } & \text{Sum of factors} & \\
1\text{ and }-28 & -27 & \\
-1\text{ and }28 & 27 & \\
2\text{ and }-14 & -12 & \\
-2\text{ and }14 & 12 & \\
4\text{ and }-7 & -3 & \text{...is what we need}\\
-4\text{ and }7 & 3 &
\end{array}\right]$
$n^{2}-3n-28=(n-4)(n+7)$
The possible dimensions of the rectangle are $n+4$ and $n-7$.
