SOLUTION: IF the perimeter of a rectangle is 72m what is the largest area

Question 167972: IF the perimeter of a rectangle is 72m what is the largest area
Found 2 solutions by stanbon, josmiceli:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
IF the perimeter of a rectangle is 72m what is the largest area
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P = 2(l+w)
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72 = 2(l+w)
l+w = 36
l = 36-w
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Area = width*length
A = w(36-w)
A = 36w - w^2
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maximum occurs when w = -b/2a = -36/(2*-1) = 18
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If w = 18 then l = 18
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Cheers,
Stan H
Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
I happen to know that a rectagle of a
certain perimeter has the largest area
when it is a square. I'll prove it
If the perimeter is , and it is a
square, each side is
The area of the square is
Now suppose it's not a square, but slightly
off like 17.9 x 18.1 That still
makes the perimeter 72.
, so
is the maximum area which occurs when
the rectangle is an 18 x 18 square
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