cool rectangle

[Nekkamath]

A rectangle is called "cool" if the number of square units in its area is equal to twice the number of units in its perimeter. A cool rectangle also must have integer side lengths. What is the sum of all the different possible areas of cool rectangles?

 

[stapel]

A rectangle is called "cool" if the number of square units in its area is equal to twice the number of units in its perimeter. A cool rectangle also must have integer side lengths. What is the sum of all the different possible areas of cool rectangles?

What have you done? How far have you gotten?

Please reply with your work and reasoning, starting with the variables you picked and the formulas you used. Thank you!

Eliz.