What is the least amount of fencing you would need in order to enclose an area of 72 square feet?
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
To find the least amount of fencing needed to enclose an area of 72 square feet, we need to calculate the perimeter of the shape. Since the shape is not specified in the question, let's assume we are enclosing a square as it usually results in the minimum perimeter for a given area.
To find the side length of the square, we square root the area. In this case, the square root of 72 is approximately 8.49 feet. Since a square has four equal sides, each side of the square would be approximately 8.49 feet long.
To calculate the perimeter, we multiply the side length by 4 (number of sides in a square). Therefore, the least amount of fencing needed to enclose an area of 72 square feet is approximately 33.96 feet.
So, you would need at least 33.96 feet of fencing to enclose an area of 72 square feet assuming you are enclosing a square.