Suppose you have 100ft of fence to make a play area for your dog. Does a square or circle provide more area? What other factors might you take into consideration in designing your play area?

Answer 1

The circle is the most efficient shape for a maximum area given some perimeter.
Here is why:
if circumf = 100
2πr = 100
r = 100/(2π) = 15.915
area = πr^2 = π(15.915)^2 = 795.77

if you had a square:
each side = 25
Area = 25x25 = 625 which is quite a bit less than the circle
Any other shape, e.g. an equilateral triangle, is less than the area of a circle.

Answer 2

Circle it has a larger area by 3 more