Answer:

The maximum area that can be enclosed is 40000 feet square.

Step-by-step explanation:

Given : If 800 feet of fencing is used to enclose a rectangular plot of land that borders a river.

To find : What is the maximum area that can be enclosed?  

Solution :

Let the width of the rectangular is x feet.

We have given 800 feet of fencing i.e. perimeter = 800 feet.

Perimeter of rectangle is P=2(l+w)

800=2(l+x)

400-x=l

The area of the rectangle is

A=ltimes w

A=(400-x)times x

A=400x-x^2

To maximize the area derivate w.r.t x

A'=400-2x

Put A’=0

400-2x=0

2x=400

x=200

i.e. width of the rectangle is x=200.

The length of the rectangle is l=400-x=400-200=200

The area of the rectangle is A=200times 200=40000ft^2

Therefore, The maximum area that can be enclosed is 40000 feet square.