# 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

SHAIK AASIF AHAMED
8 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=$\dpi{80} \sqrt{2a}$
for minimum length L =$\dpi{80} \sqrt{2a}$+2a/$\dpi{80} \sqrt{2a}$=2$\dpi{80} \sqrt{2a}$
x =$\dpi{80} \sqrt{2a}$and breadth y =(a/$\dpi{80} \sqrt{2a}$)=$\dpi{80} \sqrt{2a}$/2=x/2
x = 2y
Thanks and Regards
Shaik Aasif