SOLUTION: Find the dimensions of a rectangle (a) with the greatest area whose perimeter is 30 feet.

Question 166708: Find the dimensions of a rectangle (a) with the greatest area whose perimeter is 30 feet.
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
Find the dimensions of a rectangle (a) with the greatest area whose perimeter is 30 feet.
Area = Length * Width
Perimeter = 2L + 2W = 30
------------------
L+W = 15
W = 15-L
Area = L*W = L*(15-L)
A = 15L - L^2
To find the maximum, set the 1st derivative to zero
15 - 2L = 0
L = 7.5
W = 7.5
The max area for a rectangle is a square, always. The max area for a given perimeter is a circle.
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