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
