Question

Q. 6. A given rectangular area is to be fenced off, in a
field whose length lies along the river. Show that
the least length will be required when length of
the field is twice its breadth. ​

Answer 1

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

mark this as the brainliest if it helps!