Find the length and width of a rectangle that has the given area and a minimum perimeter. Area: 162 square feet

The width and length of rectangle is 12.728 m

Step-by-step explanation:

Let the length of the rectangle = L

let the width of the rectangle = W

The subjective function is given by;

F(p) = 2(L + W)

F = 2L + 2W

Area of the rectangle is given by;

A = LW

LW = 162 ft²

L = 162 / W

Substitute in the value of L into subjective function;

Take the second derivative of the function, to check if it will given a minimum perimeter

Determine the critical points of the first derivative;

df/dw = 0

L = 162 / 12.728

L = 12.728 m

Therefore, the width and length of rectangle is 12.728 m

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