SOLUTION: if a rectangle has a area of 247 square centimeters, what is its perimeter?
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Question 451708: if a rectangle has a area of 247 square centimeters, what is its perimeter?
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
Don't know.
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:
\ =\ 2w\ +\ 2\,\cdot\,\frac{247}{w})
But it is clear that
\ =\ \infty)
and
\ =\ \infty)
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
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