Answer to Question #148339 in Calculus for Angelo

Question #148339
If one side of a rectangular field is to have a river as a natural boundary, find the dimensions
of the largest rectangular field that can be enclosed by using 240 m of fence for the other three sides.
1
Expert's answer
2020-12-09T08:21:10-0500

The Perimeter "P" of the field is given as:

"P=2W+L\\\\ \\text{where L and W are length and width}\\\\\n240=2W+L\\\\\nL=240-2W\\\\\nA=W \\times L\\\\\nA=W(240-2W)\\\\\nA=240W-2W^2\\\\\nA'=240-4W\\\\\n\\text{set A' to 0}\\\\\n0=240-4W\\\\\nW=240\/4=60\\\\\nA''=-4\\\\\n\\text{This implies that W=60 is the maximum value}\\\\\\text{Substitute 60 for W in L=240-2W}\\\\\nL=240-120\\\\\nL=120m"


Hence the dimension of the largest rectangle field will be "60m \\times 120m".


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