Find the length and width of a rectangle that has the given

Find the length and width of a rectangle that has the given area and a minimum perimeter.

Area: 81 square feet

Solution

Area = 81

Let x be length and y be width

x*y = 81 ----(1)

Perimeter (P) = 2x+2y

P = 2x + 162/x

To have min. perimeter: dP/dx =0

dP/dx = 2 -162/x^2 =0

x = 9 feet

y = 81/x = 9 feet

Lenght = 9 feet

width = 9 feet

x = 9 feet