Final answer:
When purchasing the northwest quarter of a section of land, each side of this quarter section would be half a mile or 2,640 feet in length.
Step-by-step explanation:
When you purchase the northwest quarter of a section of land, you acquire what is traditionally known as a quarter section. A section, as defined by the Ordinance of 1785, is a square piece of land with each side being one mile long, which makes it 640 acres in total.
Consequently, a quarter section would consist of 160 acres, and since it's a square parcel, each side of the northwest quarter section would therefore be half a mile, or 2,640 feet (since there are 5,280 feet in a mile).