How do you find the dimensions and maximum area of a rectangle whose perimeter is 24 inches?

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Answer 1 · 2016-02-07T18:39:38

A #6xx6# square with area 36 square inches

The rectangle has sides h and l, perimeter p and area a:

(a) #p=2h+2l=24#

(b) #a=h*l#

(a) #h=12-l#

(b) #a=(12-l)*l= 12l-l^2#

The maximum of #a# occurs when the first derivative is zero:

#( 12l-l^2)'= 12-2l=0#
#l=12/2=6#

#h=12-6=6#