For rectangles of area 100 m^2 what is the perimeter of the rectangle with the smallest perimeter?
100=ab
P=2a+2b
P=2a+200/a
dP/da=2-200/a^2
dP/da=0 implies 2=200/a^2
a^2=100
a=-10,10
a is a length so take positive a, a=10
so b=10
gives perimeter 40m
Notice a=10 b=10 is a square
Squares are rectangles of smallest perimeter
DN
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