A rancher wants to fence in an area of 1000000 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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anonymous · Answer

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anonymous · Answer

you have $LW=1,000,000$ so $W=\frac{1,000,000}{L}$ and you want to minimize 
$$3L+W=3L+\frac{1,000,000}{L}$$

anonymous · Answer

this gives you 
$$f(L)=3L+\frac{1,000,000}{L}$$ to find the minimum, take the derivative, find the critical points by setting the derivative equal to zero, and solve for $L$

anonymous · Answer

you good from there?