Question

The back of Tom's property is a creek. Tom would like to enclose a rectangular area, using the creek as one side and fencing for the other three sides, to create a pasture. If there is 780 feet of fencing available, what is the maximum possible area of the pasture?

Answer 1

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:

$780 = L+2S\\A= LS\\\\L=780-2S\\A=-2S^2+780S$

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:

$\frac{dA}{dS}=0=-4S+780\\S= 195\\L=780-(2*195)=390$

The maximum possible area is:

$A_{MAX}=390*195=76,050\ ft^2$