Answer:
[tex]Area_{max}=11,281,250m^{2}[/tex]
Explanation:
We were given the following information:
Ed has 9,500 meters of fencing
Ed does not fence the side along the river
[tex]\begin{gathered} Perimeter=9,500m \\ Perimeter=length+2*width \\ length=9,500-2x \\ width=x \\ The\text{ area of a rectangle is given by:} \\ Area=length*width \\ Area=\lparen9,500-2x)*x \\ Area=9,500x-2x^2 \\ Area=-2x^2+9,500x \\ The\text{ maximum point occurs at the vertex \lparen to obtain the largest area that can be enclosed\rparen:} \\ x=-\frac{b}{2a}=-\frac{9,500}{2\left(-2\right)} \\ x=\frac{9,500}{4}=2,375 \\ x=2,375 \\ Substitute\text{ this into the formula for ''length'', we have:} \\ length=9,500-2\left(2,375\right) \\ length=9,500-4,750=4,750 \\ length=4,750m \\ w\imaginaryI dth=x=2,375m \\ Area_{max}=length*width \\ Area_{max}=4,750*2,375 \\ Area_{max}=11,281,250m^2 \\ \\ \therefore Area_{max}=11,281,250m^2 \end{gathered}[/tex]
Therefore, the largest area that can be enclosed is 11,281,250 sq. meters
