Answer
$\dfrac{128}{\pi^2} \text{ feet OR approximately }12.97\text{ feet}
$
Work Step by Step
Substituting $
P=4
$ in the given equation, $
P=2\pi\sqrt{\dfrac{l}{32}}
,$ results to
\begin{array}{l}\require{cancel}
4=2\pi\sqrt{\dfrac{l}{32}}
\\
\dfrac{4}{2\pi}=\sqrt{\dfrac{l}{32}}
\\
\dfrac{2}{\pi}=\sqrt{\dfrac{l}{32}}
.\end{array}
Squaring both sides, the equation above is equivalent to
\begin{array}{l}\require{cancel}
\left(\dfrac{2}{\pi}\right)^2=\left(\sqrt{\dfrac{l}{32}}\right)^2
\\
\dfrac{4}{\pi^2}=\dfrac{l}{32}
\\
l(\pi^2)=4(32)
\\
l=\dfrac{4(32)}{\pi^2}
\\
l=\dfrac{128}{\pi^2}
\\\text{OR}\\
l\approx12.97
.\end{array}
Hence, the length, $l,$ is $
\dfrac{128}{\pi^2} \text{ feet OR approximately }12.97\text{ feet}
.$
