If 400 feet of fencing is used to enclose a rectangular plot of land that borders a river, what is the maximum area that can be

Question

gregori [183]

3 years ago

13

If 400 feet of fencing is used to enclose a rectangular plot of land that borders a river, what is the maximum area that can be

enclosed? answer to the nearest square foot without commas. for example, if the answer is 1,000, write 1000.

Mathematics

2 answers:

Marizza181 [45] · Answer 1 · 2022-08-07T16:34:17+03:00

Let say the length of the rectangle is x. The material that can be used would determine the perimeter of the rectangle. Using the perimeter formula you can find the rectangle width

perimeter= 2(width+length)
400= 2(width + x)
200= width+x
width= 200-x

The function to determine the area would be:
area= length * width
area= x* (200-x)
area= 200x- x^2

To find the highest area you need to find out the vertex by finding the value of x when the differentiate of the function equal to zero.
dx/dy= 200- 2x = 0
2x= 200
x=100

If you put x=100 into the area function you will find
area= 200x- x^2
area= 200(100)- (100)^2
area= 20,000 - 10,000= 10000 feet^2