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Old 07-30-2007   #1
s4apple
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A rancher wants to fence in an area of 1500000 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?
 
Old 07-30-2007   #2
EMERGENCY
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YOU GOTTA DO CALCULUS TEEE HEEEE. I could do this but if you look in your book theres an example exactly like this.
 
Old 07-30-2007   #3
Popo B
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I think the shortest possible length will be achieved if the field is a square(which is also a rectangle). So, the length of one side would be: √1500000 = 1224.74Therefore, the length of fencing required would be:1224.74*5 [4 sides + the one in the middle]=30618.62 ft//
 
Old 07-30-2007   #4
Engineer-Poet
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6000 feet of fence.Let L be the length of fence, W the width of the area, D is the depth. The width is divided in half by the middle part of the fence.W = 1,500,000 / DL = 2 W + 3 D = 3,000,000 / D + 3 DdL = 3 - 3,000,000 / D^2 The length of fence is at a minimum when dL = 0. 3 - 3,000,000 / D^2 = 0Â* Â* Â* Solve for D3 D^2 = 3,000,000D = 1000W = 1500, L = 2W + 3D = 6000
 
 

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