Answer:
See below for step-by-step proof.
Step-by-step explanation:

























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)
Side-Side-Side Theorem, Side-Angle-Side, Angle-Angle-Side, Angle-Side-Angle, and Hypotenuse-Leg for right triangles.
For example, for Side-Side-Side, if you prove all 3 sides of the triangle are congruent, then the triangle is congruent.