Question 1125332
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They want you find the minimum  x+y under condition  xy = 16.


Then y = {{{16/x}}};   x + y = {{{x + 16/x}}}.


The function  f(x) = {{{x + 16/x}}}   has the derivative  f'(x) = {{{1}}} - {{{16/x^2}}} = {{{(x^2 - 16)/x^2}}}.


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

which implies  x= {{{sqrt(16)}}} = 4.


Then y = {{{16/4}}} = 4.


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