Answer
$\dfrac{72}{\pi^2} \text{ feet OR approximately }7.30\text{ feet}
$
Work Step by Step
Substituting $
P=3
$ in the given equation, $
P=2\pi\sqrt{\dfrac{l}{32}}
,$ results to
\begin{array}{l}\require{cancel}
3=2\pi\sqrt{\dfrac{l}{32}}
\\
\dfrac{3}{2\pi}=\sqrt{\dfrac{l}{32}}
.\end{array}
Squaring both sides, the equation above is equivalent to
\begin{array}{l}\require{cancel}
\left(\dfrac{3}{2\pi}\right)^2=\left(\sqrt{\dfrac{l}{32}}\right)^2
\\
\dfrac{9}{4\pi^2}=\dfrac{l}{32}
\\
l(4\pi^2)=9(32)
\\
l=\dfrac{9(32)}{4\pi^2}
\\
l=\dfrac{9(\cancel4\cdot8)}{\cancel4\pi^2}
\\
l=\dfrac{72}{\pi^2}
\\\text{OR}\\
l\approx7.30
.\end{array}
Hence, the length, $l,$ is $
\dfrac{72}{\pi^2} \text{ feet OR approximately }7.30\text{ feet}
.$
