Question

If 800 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

p + 2 q = 800 so p = 800 - 2 q

A = p q = (800 - 2q)q

A = -2 q^2 + 800 q
now you could find the vertex of this parabola easily with Algebra 2 by completing the square but you said calculus so
dA/dq = 0 at max = -4 q + 800
or
q = 200
then
p = 800 - 400 = 400
so
A = 80,000 ft^2 or about two acres

Answer 2

80,000 ft^2 just like how we gonna go back to back