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Home Q & A Board Science-Related Homework Help Mathematics
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feeju feeju
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12 years ago
How do I go about this question. 43m of fencing, and 3 out of 4 sides are closed in. What dimensions will give me the most area (apparently the answer is 11.5m * 23m), but how did they get that? Please show all formulas and work.
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MikeLakeMikeLake
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12 years ago
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12 years ago
did u not mean 46m fencing?..in which case let 2 sides have length a..other side=46-2a..
>enclosed area A=(46-2a)*a=46a-4a^2..dA/da=46-4a.. max a when dA/da=0..ie a=11.5m
> other side has dim=46-2a=23m..and A enclosed=23*11.5
or if u bend fence in2 semicirc, u can 'enclose' A=pir^2/2=pi/2*(43/pi)^2=43^2/(2*pi)= 294.28m^2
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