[tex]\bf \textit{perimeter of a rectangle}\\\\
P=2l+2w\quad
\begin{cases}
l=length\\
w=width\\
-----\\
l=\frac{1}{4}w-6
\end{cases}\implies P=2\left( \frac{1}{4}w-6 \right)+2w
\\\\\\
P=\cfrac{1}{2}w-12+2w\implies P=\cfrac{w}{2}-12+2w\implies P=\cfrac{w-24+4w}{2}
\\\\\\
P=\cfrac{5w-24}{2}\implies P=\cfrac{5}{2}w-12[/tex]
