Arancher wants to fence in an area of 3,000,000 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?

shortest length of fence is 8485.2 ft

Step-by-step explanation:

Given data

area =  3,000,000 square feet

to find out

shortest length of fence

let length L and width is W

so area is L × W

W = 3 × /L    ............1

2W = 6 × /L

rectangular field and then divide it in half

so fencing will be 3 × L + 2 × W

i.e.  3 L + 2W

fencing =  3 L  + 6 × /L

fencing minimum = 3 L  -  6 × /L²

fencing minimum length will be zero

3 L  -  6 × /L² = 0

3 L² = 6 ×

L² =  2 ×

L  =  1414.2

so from equation 1

W = 3 × /L

W = 3 × /1414.2

W = 2121.3

so fencing will be  3 L +2 W

so fencing =   3 × 1414.2  +2 × 2121.3

fencing =  4242.6 +4242.6

fencing =  8485.2

shortest length of fence is 8485.2 ft