What is the greatest difference in the perimeters of two rectangles whose sides have integral lengths and whose areas are both 25?

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What is the greatest difference in the perimeters of two rectangles whose sides have integral lengths and whose areas are both 25?

Mathematics
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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smallest rectangle would be a square, largest would be 1X25 --> 52 -20 = 32
Correct! (would prefer a more cogent solution but that's okay :))
Here come another test for your mathematical mettle.

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wasn't sure if it was needed here
It wasn't but others may look and want to know how to solve such problems. It's your call.
i'll just say that a square of some given area always minimizes the perimeter
may be if the product is of the two variables is constant, the sum of the variables will be minimum when they are equal?
Yes, or as close together as possible.

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