Find all sides of rectangle having integral sides whose area is numerically equal to perimeter?
I also want the mathematical proof

2. Let a and b be the sides of the rectangle. Then

$2a+2b=ab\Rightarrow a=\frac{2b}{b-2}=2+\frac{4}{b-2}$

Then $b-2$ must be a positive divisor of 4.

Take all possible cases: b-2=1, b-2=2, b-2=4. Find b and then find a.