Find the dimensions of a rectangle with area 2,197 m2 whose perimeter is as small as possible. (if both values are the same number, enter it into both blanks.) m (smaller value) m (larger value)

The dimensions of the rectangle are:

Step-by-step explanation:

Let x be the length and y be the width of the rectangle.

According with the graph the area is and its perimeter is

Solving the area function for y gives us

Plug this into the perimeter function

Because we want to minimize the perimeter function, find the derivative and set it equal to zero to locate the critical points.

Because a width cannot be negative we only take as a valid solution:

After establishing the critical points of this function, the second derivative test uses the value of the second derivative at those points to determine whether such points are a local maximum or a local minimum.

If , then f has a local minimum at

The second derivative is

Plug into the second derivative

Because , is a local minimum.

The dimensions of the rectangle are:

the correct answer is 828.07