Find the dimensions of a rectangle (in m) with area 1,331 m2 whose perimeter is as small as possible. (Enter the dimensions as a comma separated list.)

The dimensions of the rectangle are x = 36.48 m and  y = 36.48 m

Step-by-step explanation:

Let the sides of the rectangle be x and y

Objective function is given by;

F = 2(x + y)

F = 2x + 2y

The area of the rectangle is given by;

xy = 1331

y = 1331 / x

Substitute in the value of y in objective function;

Determine the derivative of the function;

Find the critical points;

F' = 0

Take the second derivative of the function

Determine the second dimension;

y = 1331 / x

y = 1331 / 36.48

y = 36.48m

Therefore, the dimensions of the rectangle is x = y = 36.48 m

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