anonymous
  • anonymous
A gardener has 200 meter of fencing to enclose two adjacent rectangular plots.What dimensions will produce a maximum enclosed area?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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AkashdeepDeb
  • AkashdeepDeb
WELCOME TO OPENSTUDY.!!! :D
AkashdeepDeb
  • AkashdeepDeb
Now this question is a bit trial and error. So they say that the gardener has 200m as the perimeter rught? So 2(Length + Breadth) = 200 So Length + Breadth = 100 Now we cannot measure ALL the possibilities here but It is is observed that Length * Breadth = Greatest [Length + Breadth = 100] 48 * 52 = 2496 49 * 51 = 2499 50 * 50 = 2500 [MAXIMUM] Understood? I cannot think of a better way! :)
blockcolder
  • blockcolder
There's always calculus and the first derivative test.

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AkashdeepDeb
  • AkashdeepDeb
I am not familiar with that. Maybe you can explain it to him then! :D
blockcolder
  • blockcolder
Alternatively, there's the AM-GM inequality: \[\sqrt{LW}\leq\frac{L+W}{2}\] with equality iff L=W, for all positive L and W.
blockcolder
  • blockcolder
Thus, \[\sqrt{LW}\leq\frac{100}{2}\Rightarrow\sqrt{LW}\leq50 \Rightarrow LW\leq2500\] which means LW can only reach up to 2500, if L+W=100, and this happens when L=W=50.

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