Question

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.

Answer 1

20000

Explanation:

Since the fencing borders a river we know the formula for the perimeter is P=L+2w

400=L+2w

L=400-2w

Plug this into the area

A=Lw

A=w(400-2w)

A=400w-2w^2

A'=-4w+400

set the derivative to 0

-4w+400=0

w=100

A=100(400-2(100))

A=20000