Final answer:
The length l of a rectangular field varies inversely as its width w can be expressed as the equation l = k/w, where k is the constant of variation.
Step-by-step explanation:
To express the statement 'The length l of a rectangular field varies inversely as its width w' as a mathematical equation, we can say that the product of the length and the width of a rectangle is constant.
An inverse variation can be written as: l = k/w, where k is the constant of variation. As the width w increases, the length l decreases such that their product remains constant.
To see this in an example, if the width of a rectangular field is doubled, the length would be halved to maintain the same area, demonstrating the inverse relationship between the two dimensions.