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
