Answer
The possible dimensions of the rectangle are $x+8$ and $x-9$.
Work Step by Step
To factor $x^{2}-x-72$, identify the pair of factors of $-72$ that has a sum of $-1$.
$\left[\begin{array}{lll}
\text{Factors of -72 } & \text{Sum of factors} & \\
1\text{ and }-72 & -71 & \\
-1\text{ and }72 & 71 & \\
2\text{ and }-36 & -34 & \\
-2\text{ and }36 & 34 & \\
3\text{ and }-24 & -21 & \\
-3\text{ and }24 & 21 & \\
4\text{ and }-18 & -14 & \\
-4\text{ and }18 & 14 & \\
6\text{ and }-12 & -6 & \\
-6\text{ and }12 & 6 & \\
8\text{ and }-9 & -1 & \text{...is what we need}
\end{array}\right]$
$x^{2}-x-72=(x+8)(x-9)$
The possible dimensions of the rectangle are $x+8$ and $x-9$.
