What are the dimensions of a rectangular field of area A that requires the least amount of fencing?
4 answers
a square
Are you saying that the answer is lw?
Does this problem have a solution? Could you please type it in for me. Thanks! :)
Huh, you can't figure the dimensions of s square of area A?
The maximum area for a given perimeter is a square.
The minimum perimeter for a given rectangular area is a square.
So, the length and width would both be √A
But, since you seem to be taking calculus, look at the dimensions. If the width is x, the length is A/x
The perimeter is
p = 2(x + A/x)
dp/dx = 2(1 - A/x^2)
dp/dx = 0 when 1 - A/x^2 = 0
That is, when x = √A
as we started out.
The maximum area for a given perimeter is a square.
The minimum perimeter for a given rectangular area is a square.
So, the length and width would both be √A
But, since you seem to be taking calculus, look at the dimensions. If the width is x, the length is A/x
The perimeter is
p = 2(x + A/x)
dp/dx = 2(1 - A/x^2)
dp/dx = 0 when 1 - A/x^2 = 0
That is, when x = √A
as we started out.
2 answers