SOLUTION: Alexa drew a rectangle with an area of 36 square centimeters. The rectangle she drew has the smallest perimeter possible for this area. What is the length and width of the recta

Algebra ->  Rectangles -> SOLUTION: Alexa drew a rectangle with an area of 36 square centimeters. The rectangle she drew has the smallest perimeter possible for this area. What is the length and width of the recta      Log On


   

Question 967086: Alexa drew a rectangle with an area of 36 square centimeters. The rectangle she drew has the smallest perimeter possible for this area. What is the length and width of the rectangle she drew?
Answer by stanbon(75887) About Me  (Show Source):
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Alexa drew a rectangle with an area of 36 square centimeters. The rectangle she drew has the smallest perimeter possible for this area. What is the length and width of the rectangle she drew?
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Area:: L*W = 36 cm^2
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Perimeter:: P = 2L + 2W
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Equation::
P = 2(36/W) + 2W
P = (72/W) + 2W
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Find the minimum "P"::
P' = -72/W^2 + 2
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Solve:: -72/W^2 + 2 = 0
-72/W^2 = -2
W^2 = 36
W = 6 cm (Width)
Length = 36/6 = 6 cm
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Cheers,
Stan H.
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