[tex]\begin{cases} 16= w+l \\ 48= w \cdot l\end{cases}\\\\\begin{cases}l= 16- w \\ 48= w \cdot (16-w)\end{cases}\\\\\begin{cases}l= 16- w \\ 48 = 16w-w ^2 \end{cases}\\\\ w^2 -16w -48=0[/tex]
[tex]a= 1, \ \ b=-16, \ \c = 48 \\\\\Delta =b^2-4ac = 16^2 -4\cdot(-1)\cdot (-48) = 256-192 =64 \\ \\w_{1}=\frac{-b-\sqrt{\Delta} }{2a}=\frac{16-\sqrt{64}}{2 }=\frac{16-8}{2}=\frac{8}{2}=4 \\\\w_{2}=\frac{-b+\sqrt{\Delta} }{2a}=\frac{ 16+8}{2}=\frac{24}{2}=12[/tex]
[tex]\begin{cases} l= 16- 4 \\ w=4 \end{cases} \ \ or \ \ \begin{cases} l= 16- 12 \\ w=12\end{cases} \\ \\\begin{cases} l= 12 \ m \\ w=4 \ m \end{cases} \ \ or \ \ \begin{cases} l= 4 \ m \\ w=12\end{cases}[/tex]
