[tex]\bf \stackrel{\textit{perimeter of a rectangle}}{P=2L+2W\implies 2(L+W)}~~
\begin{cases}
L=length\\
W=width\\
--------\\
P=84\\
L=\stackrel{\textit{twice the width}}{2W}
\end{cases}
\\\\\\
84=2(L+W)\implies \cfrac{84}{2}=L+W\implies 42=L+W
\\\\\\
42=(2W)+W\implies 42=3W\implies \cfrac{42}{3}=W\implies 14=W[/tex]
