SOLUTION: A wire that is 500M long is used to fence a rectangular field. What are the dimensions of the largest possible rectangular field that can be fenced using the wire? Note: The larges
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Question 1056146: A wire that is 500M long is used to fence a rectangular field. What are the dimensions of the largest possible rectangular field that can be fenced using the wire? Note: The largest field that can be fenced is the one with the greatest area.
Answer by htmentor(1343) (Show Source): You can put this solution on YOUR website!
The area of the rectangular field, A = l*w
The perimeter of the fenced in area is 2(l+w) = 500 m
Express w in terms of l: w = 250 - l
Therefore A = l(250-l)
The largest area will be obtained where dA/dl = 0 = 250 - 2l
Solve for l:
l = 250/2 = 125 m
w = 250 - 125 = 125 m
So length and width are both 125 m, i.e. a square
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