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