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.