SOLUTION: Find the length and width (in feet) of a rectangle that has the given area and a minimum perimeter. Area: 16 square feet

Question 1125332: Find the length and width (in feet) of a rectangle that has the given area and a minimum perimeter.
Area: 16 square feet
Answer by ikleyn(52776) (Show Source): You can put this solution on YOUR website!
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They want you find the minimum  x+y under condition  xy = 16.


Then y = ;   x + y = .


The function  f(x) =    has the derivative  f'(x) =  -  = .


The derivative is zero when  x^2 - 16 = 0,   or   x^2 = 16,

which implies  x=  = 4.


Then y =  = 4.


Answer.  The square (4 feet x 4 feet) gives the minimal perimeter, which is 16 feet.

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