What is the least amount of fencing you would need in order to enclose an area of 72 square feet?

Answer 1

Hi I think this is how it should be done, not completely sure please check other scources as well

For this question to be answered at least a basic shape is required, is it a rectangle, is it a circle.

The optimisation of the perimeter of a rectangle or square could be found assuming there are no other specifications

by saying the area
is xy=72

therefore y=72/x

The perimeter is
2x+2y=p

substitute y from the area

2x+2(72/x)=p

2x +144(1/x) =p

because Perimeter is the minimum
use differencitaion

0= 2 + 144(-1/x^2)

0= 2 - 144/x^2

2= 144/x^2
2x^2 = 144
x^2 = 72

x = Square root of 72

therefore the optimum perimeter would be 4 times the square root of 72