Explain why the perimeter:Area ratio value can be used to understand cost effectiveness

Answer 1

perimeter defines the length and therefore cost of fencing.
area defines the size of the enclosure, for example how much grass for the cows to munch.
the minimum fence length for maximum grass is the perimeter to area ratio.
Example for rectangle:
What are the dimensions of a rectangular field that surrounds the maximum area with 100 meters of fence?
x+y = 50
A = x y

if it is square:
25 on a side
area = 625

if one side is longer, for example 10 by 40
area = 400

least fence cost for square, x/y = 1
perimeter/area = 4 x/x^2 = 4/x

Answer 2

to find the total area under sq.feet