We have the next equation for the Area
the formula for the area is
[tex]A=l\times w[/tex]l=650-2x
w=x
then we substitute the values
[tex]A=(650-2x)(x)[/tex][tex]A=650x-2x^2[/tex]the maximum value of x is the vertex of the quadratic equation
where
a=-2
b=650
[tex]x=\frac{-b}{2a}=\frac{-650}{2(-2)}=\frac{-650}{-4}=162.5[/tex]the largest area that can be enclosed is
[tex]\begin{gathered} A=650(162.5)-2(162.5)^2 \\ A=105625-52812.5 \\ A=52812.5m^2 \end{gathered}[/tex]l=650-2(162.5)=325m
w=162.5m
