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A given rectangular area is to be fenced off in a field whose length lies along astraight river. If no fencing is needed along the river, show that the least length offencing will be required when length of the field is twice its breadth

prashant kashya , 10 Years ago
Grade upto college level
anser 1 Answers
SHAIK AASIF AHAMED

Last Activity: 10 Years ago

Hello student,
let length be x m and breadth be y m.
length of fence L = x+2y
Let given area is a=xy or y =a/x
L = x + 2a/x
dL/dx= 1-2a/x2
dL/dx=0
so x=\sqrt{2a}
for minimum length L =\sqrt{2a}+2a/\sqrt{2a}=2\sqrt{2a}
x =\sqrt{2a}and breadth y =(a/\sqrt{2a})=\sqrt{2a}/2=x/2
x = 2y
Thanks and Regards
Shaik Aasif
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