Find the dimensions of a rectangle with area 2,197 m2 whose perimeter is as small as possible.

The area of a rectangle is calculated by multiplying its length and width. That is,
                               A = L x W
Given that area is 2,197, the width is 2197/L. The perimeter on the other hand is the twice the sum of the dimensions. That is,
                         P = 2L + 2(2197/L)
Differentiating the equation and equating the differential to zero. 
                       dP = 2 + 4394(-1/L²) = 0
Solving for L will give us an answer of 46.87 m. Thus, the length and the width of the rectangle are approximately 46.87 m both.