A rancher 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?

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DeniceSandidge DeniceSandidge · Answer 1 · 2019-07-31T12:22:48+02:00

Answer:

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 × [tex]10^{6}[/tex] /L ............1

2W = 6 × [tex]10^{6}[/tex] /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 × [tex]10^{6}[/tex] /L

fencing minimum = 3 L - 6 × [tex]10^{6}[/tex] /L²

fencing minimum length will be zero

3 L - 6 × [tex]10^{6}[/tex] /L² = 0

3 L² = 6 × [tex]10^{6}[/tex]

L² = 2 × [tex]10^{6}[/tex]

L = 1414.2

so from equation 1

W = 3 × [tex]10^{6}[/tex] /L

W = 3 × [tex]10^{6}[/tex] /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