Is there a relationship between area or perimeter of a rectangle

Hello,

For a given perimeter (P) there are an infinity of Area (A)

Let's say x the length, and y the wide of the rectangle

P=2 (x+y)

A=xy

k=x-y >=0

As (x+y) ²-4xy = (x-y) ²: A²-4P=k² or P = (A²-k²) / 4

In primus, you will find a graph (abacus) giving P for a A and k given.

Negative Area or P are excluded. (just remind the first quadrant, A>=0 and P>=0)