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

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

Grade:upto college level

1 Answers

SHAIK AASIF AHAMED
askIITians Faculty 74 Points
7 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
askIITians faculty

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