SOLUTION: A rectangle has a perimeter of 100cm find the greatest possible area for the rectangle

Question 700126: A rectangle has a perimeter of 100cm find the greatest possible area for the rectangle
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
A rectangle has a perimeter of 100cm find the greatest possible area for the rectangle
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Perimeter = 2L + 2W so
L + W = 50
and L*W = area
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Start with L = W:
Area = L*W = = 25*25 = 625
For any others:
Area = (L-x)*(W+x) = 625 - x^2
The obvious max is at x = 0
--> max area at L = W
max Area = 625
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the hard way:
Area = L*(50 - L)
Area = 50L - L^2
That's a parabola with a max at its vertex
The L at the vertex is L = -b/2a
L = -50/2 = 25
L = 25
W = 25
Area = 625 sq cm

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