A rectangular field has a length that is twice its width. Within this field, there is a square pond with each side measuring 8 meters. If the pond's area is one-eighth of the total area of the field, what is the length of the field?

Explanation

Let the width of the field be x meters, so the length is 2x meters. The area of the field is 2x * x = 2x². The pond is a square with side 8 meters, so its area is 8 * 8 = 64 m². Given that the pond's area is one-eighth of the field's area, we have 64 = (1/8) * 2x². Solving this gives 64 = (2x²)/8, which simplifies to 64 = x²/4, so x² = 256 and x = 16 meters. Therefore, the length of the field is 2 * 16 = 32 meters.