If a field has perimeter P, what shape maximizes the area? Justify your reasoning.

Answer 1

Let's suppose the perimeter is 100 meters.

If it was 2 by 48 meters, the area would be would be 196 square meters

If it was 20 by 30 meters, the area would be 600 square meters.

If it was 25 by 25, the area would be 625 square meters.

Answer 2

But, what shapes are those measurements?

Answer 3

If a rectangle has four sides of equal length, what shape is it?

Answer 4

If all shapes have the same perimeter a circle will be the shape that would maximize the area.