Afarmer wants to build a pen for his sheep. one side of the pen will be a river. the sheep need about 2000 m2 of area to graze. about what length (x) and width (y) should the organization use to use the least amount of fencing possible?

The way I did it before I knew calculus, was that when legnth=width, you get max area with minimumperimiter
so L=W= √2000=20√5

legnth and width should be 20√5 meters

the following is calculus
xy=2000  and 2(x+y)=P
solve
ok so
xy=2000
divide both sides by x
y=2000/x
sub 2000/x for y in other equation

2(x+2000/x)=P
2x+4000/x=P
to find the minimum value of this, take the derivitive and find where it equals 0
2-4000/(x^2)=0
2=4000/(x^2)
2x^2=4000
x^2=2000
x=√2000
x=20√5
y=2000/x
y=2000/(√2000)
y=√2000=20√5

x=y=20√5 meters