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How do you find the length and width of a rectangle whose area is 900 square meters and whose perimeter is a minimum?

1 Answer

Jun 11, 2015

Length = Width = 30 meters

Explanation:

If #LxxW = 900#
#rArr L= 900/W#

#P = 2*(L+W)#

#color(white)("XX")##= 2(900/W +W)#

#color(white)("XX")##=1800W^(-1) + 2W#

The minimum will occur when #(dP)/(dW) =0#

#(dP)/(dW) = -1800W^(-2) +2 = 0#

#color(white)("XXXX")#1/W^2 = (-2)/(-1800)#

#color(white)("XXXX")##W^2 = 900#

#color(white)("XXXX")##W =30#

and since #LxxW =900#
#rArr L =30#

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