Answer:
6000 ft
Step-by-step explanation:
Let length of rectangular field=x
Breadth of rectangular field=y
Area of rectangular field=
square ft
Area of rectangular field=
Area of rectangular field=


Fencing used ,P(x)=
Substitute the value of y
P(x)=

Differentiate w.r.t x

Using formula:





It is always positive because length is always positive.
Again differentiate w.r.t x

Substitute x=1500

Hence, fencing is minimum at x=1 500
Substitute x=1 500

Length of rectangular field=1500 ft
Breadth of rectangular field=1000 ft
Substitute the values
Shortest length of fence used=
Hence, the shortest length of fence that the rancher can used=6000 ft