[tex]\bf \textit{area of a rectangle}\\\\
A=lw\quad
\begin{cases}
l=length\\
w=width\\
-----\\
A=285
\end{cases}\implies 285=lw\implies \boxed{\cfrac{285}{w}=l}
\\\\\\
\textit{perimeter of a rectangle}\\\\
P=2(l+w)\quad
\begin{cases}
l=\frac{285}{w}\\\\
P=68
\end{cases}\implies 68=2\left( \boxed{\cfrac{285}{w}}+w \right)
\\\\\\
\cfrac{68}{2}=\cfrac{285}{w}+w\implies 34=\cfrac{285+w^2}{w}\implies 34w=285+w^2[/tex]
[tex]\bf 0=w^2-34w+285\implies 0=(w-19)(w-15)\implies w=
\begin{cases}
19\\
15
\end{cases}
\\\\\\
\stackrel{lenght}{l}=
\begin{cases}
\frac{285}{19}\implies &15\\\\
\frac{285}{15}\implies &19
\end{cases}[/tex]
