Arancher wants to fence in an area of 15 square feet in a rectangular field and then divide it in half with a fence down the middle parallel to one side. what is the shortest length of fence that the rancher can use? note: the answer to this problem requires that you enter the correct units. (enter your answer with a space before the units)

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

a negative exponent is translated as follows:

so, we have