[tex]\bf \textit{area of a rectangle}\\\\ A=Lw~~ \begin{cases} L=length\\ w=width\\[-0.5em] \hrulefill\\ A=4x+32\\ L=4 \end{cases}\implies 4x+32=4w \\\\\\ \cfrac{4x+32}{4}=w\implies \cfrac{~~\begin{matrix} 4 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~ (x+8)}{~~\begin{matrix} 4 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}=w\implies \boxed{x+8=w}[/tex]
