Jack has 800 feet of fencing to fence off a rectangular field that borders a straight river. HE DOESN'T NEED TO FENCE ALONG THE RIVER. What are the dimensions( L and W ) of the field that has the largest area? What is the largest area?

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Jack has 800 feet of fencing to fence off a rectangular field that borders a straight river. HE DOESN'T NEED TO FENCE ALONG THE RIVER. What are the dimensions( L and W ) of the field that has the largest area? What is the largest area?

Mathematics
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So, you are trying to fence an area next to a river. As you don't need to fence the rive, you can save one side of the rectangle and add more to the other tree sides L __________________ | | W | | W | | ~~~~~~~~~~~~~~~~~~~~~~~ river We have 800 ft of fence to cover 2W + L so, (1) 2W + L = 800 As a rectangle we can assume: (2) L = 2W As we saved the river side of fence the maximum area we can achieve is: (3) A = (2W)(L) Therefore you have 3 equations (1), (2) and (3) and three unknowns L, W, A. Can you solve?
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I ended up getting all that, so does that mean that it comes out to roughly 266 feet for each? Great answer btw.

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Other answers:

2W+L=800 and we want to maxmize the area area=WL L=800-2W so area=W(800-2W)=800W-2W^2 area'=800-4W to find critcal numbers set area'=0 800-4W=0 4W=800 W=200 and L-800-2(200)=400 so maximum area is 400(200)=80000
ops, i had a type on my (3) Area equation it's A = WL. And Myininaya got the solution! thanks haha

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