Answer:
76,050 ft²
Step-by-step explanation:
If the area must be rectangular, let L be the length of the side opposite to the creek, and S be the length of the remaining two sides.
The perimeter of the fencing and the area of the pasture are:
[tex]780 = L+2S\\A= LS\\\\L=780-2S\\A=-2S^2+780S[/tex]
The value of S for which the derivate of the area function is zero is the length of S that maximizes the area of pasture:
[tex]\frac{dA}{dS}=0=-4S+780\\S= 195\\L=780-(2*195)=390[/tex]
The maximum possible area is:
[tex]A_{MAX}=390*195=76,050\ ft^2[/tex]
