Answer :
Let the width be x and the length be y as shown in the figure.
The perimeter of the fence is 246 feet so it follows:
[tex]\begin{gathered} 3x+2y=246 \\ y=\frac{246-3x}{2} \end{gathered}[/tex]The area of the fence is given by:
[tex]\begin{gathered} A=xy \\ A=x(\frac{246-3x}{2}) \\ A=123x-\frac{3}{2}x^2 \end{gathered}[/tex]Differentiate w. r. t. x to get:
[tex]\frac{dA}{dx}=123-3x[/tex]For maxima and minima calculation, the derivative is zero so it follows:
[tex]\begin{gathered} 123-3x=0 \\ 3x=123 \\ x=\frac{123}{3}=41 \end{gathered}[/tex]So the width is 41 feet and the length y is given by:
[tex]y=\frac{246-3(41)}{2}=\frac{123}{2}=61.5[/tex]So the width is 41 feet and length is 61.5 feet, the area covered is 2521`.5 sq feet.
