Find all sides of rectangle having integral sides whose area is numerically equal to perimeter?

I also want the mathematical proof

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- Sep 30th 2009, 06:34 AManshulbshahPlease help....tricky question
Find all sides of rectangle having integral sides whose area is numerically equal to perimeter?

I also want the mathematical proof - Sep 30th 2009, 06:53 AMred_dog
Let a and b be the sides of the rectangle. Then

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

Then $\displaystyle b-2$ 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.