Asked by Anonymous
What is the least amount of fencing you would need in order to enclose an area of 72 square feet?
Answers
Answered by
anon
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
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
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