Answer
$7x-24$.
Work Step by Step
The area of the rectangle is $$A= 21 x^2-37 x-120$$ and the length of the shortest side is $$w= 3 x+5$$.We know that the area of a rectangle is $A= l\times w$. The length of the missing side is given by: \begin{equation}
\begin{aligned}
l&= \frac{A}{w}\\
&=\frac{21 x^2-37 x-120}{3 x+5}.
\end{aligned}
\end{equation}
Use long division. $$
\begin{array}{r}
7x-24\phantom{)} \\
3x+5{\overline{\smash{\big)}\,21 x^2-37 x-120\phantom{)}}}\\
\underline{-~\phantom{(}(21x^2+35x)\phantom{-b)}}\\
0-72x-120\phantom{)}\\
\underline{-~\phantom{()}(-72x-120)}\\
0\phantom{)}
\end{array}
$$ The missing length is $7 x-24$.
