Question

What is the difference between the greatest and least possible areas of the rectangle

Answer 1

This is the most-fun kind of question there is ... the kind where it gives you
nothing to go on, so you're free to make stuff up and practically write your
own question, and then go on to answer the question that you invent.

In order to answer ANY math question, you have to take the information
you're given, and use it to find what the question asks you for.

This question gives us absolutely nothing, so I'm going to invent the given part.

Given:  The perimeter of a rectangle is 'P' .

What is the greatest possible area of the rectangle ?
What is the least possible area ?
What is the difference between the greatest and least possible areas ?

-- The greatest possible area is when you take the perimeter and make
a square out of it.  Then each side of the square is (P/4), and the area
is  (P/4)²  or  P²/16.

-- There is no least possible area. The longer and skinnier you make the
rectangle, the smaller its area becomes.  No matter how small I make the
area, you can make it smaller. You can make the area as small as you
want it to be.  You just can't make it zero.

-- The difference between the greatest and least possible areas is

  (P/4)²  minus  (the smallest number you can think of that's more than zero).