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)