jmc

Let the longer side have length $a$ and the shorter side have length $b$. We have the two equations $$\begin{array}{rl}2a+2b& =42\\ ab& =108\end{array}$$ From Equation (1), we have $a+b=21$, so $a=21-b$. Substituting that into Equation (2) to eliminate $a$, we get $$\begin{array}{rl}(21-b)(b)& =108\\ 21b-b^2& =108\\ b^2-21b+108& =0\end{array}$$ Factoring the equation, we get $(b-9)(b-12)=0$, so $b=9$ or $b=12$. $b=12$ corresponds to the longer side, so the length of the shorter side is $\boxed{9}$ feet.