Let \(\ell\) the length and \(w\) the width. By the ratio of the sides:
\(\dfrac{w}{\ell}=\dfrac{4}{7}\Longrightarrow \dfrac{w}{31.5}=\dfrac{4}{7}\Longrightarrow w=\dfrac{4\cdot31.5}{7}\Longrightarrow \boxed{w=18~in.}\)
Now, we'll find the perimeter p. We'll use the formula below:
\(p=2(\ell+w)\\\\
p=2(31.5+18)\\\\
p=2\cdot49.5\\\\
\boxed{p=99~in.}\)
The area of a rectangle is \(S=w\cdot\ell\). Then:
\(S=w\cdot\ell\\\\
S=18\cdot31.5\\\\
\boxed{S=567~in.^2}\)
