SOLUTION: A farmer wishes to fence a total area of 50m^2. If both the length (l) and width (w) must be at least 2m in length, find the dimensions of the paddock which will maximise the peri
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Question 1061786: A farmer wishes to fence a total area of 50m^2. If both the length (l) and width (w) must be at least 2m in length, find the dimensions of the paddock which will maximise the perimeter and evaluate the perimeter
This is what I have so far. I'm not sure if I'm on the right track:
Area= wl= 50m^2
w= 50/l
You can put this solution on YOUR website! A farmer wishes to fence a total area of 50m^2. If both the length (l) and width (w) must be at least 2m in length, find the dimensions of the paddock which will maximise the perimeter and evaluate the perimeter
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The minimum perimeter for a rectangle is a square.
The max for this would be 2m by the other dimension.
--> 2 by 25
P = 2W + 2L = 54 meters
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To be rigorous:
L*W = 50 --> W = 50/L
P = 2W + 2L = 2L + 100/L
dP/dL = 2 - 100/L^2 = 0
2L^2 - 100 = 0
L = sqrt(50) meters is the minimum for the given area.
There is no maximum for L.
eg, L = 100 --> W = 0.5 --> P = 201
Any combination of L & W where L*W = 50 is greater than L = W = sqrt(50)
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Only the restriction of a minimum of 2 limits it to P = 54
