Question

What are the dimensions of a rectangular field of area A, that requires the least

amount of fencing?

Answer 1

length of fencing:

$L=2(x+y)$

area:

$A=xy\implies y=A/x$

$L=2(x+A/x)$

$L'(x)=2(1-A/x^2)=0$

$x=y=\sqrt A$