The smallest perimeter would be obtained if the rectangle were a square with sides measuring which would have a perimeter of . (For a small fee, I can give you the proof that for a given perimeter, the maximum area is the square of the perimeter divided by 4, which tells us conversely that for a given area the minimum perimeter is four times the square root of the area -- write back if you are interested)
But if the rectangle were any other shape, the area being means that . Substituting into the Perimeter formula gives us perimeter as a function of width:
But it is clear that
and
Therefore all you can say about the perimeter given only the specific area of 247 is:
And in general,
John
My calculator said it, I believe it, that settles it
