Final answer:
The correct measurements of a quarter section of land are 1/2 mile by 1/2 mile, which equals an area of 160 acres.
Step-by-step explanation:
The measurements of a quarter section of land are essential for understanding land division in the United States surveying system. By definition, a quarter section is a subdivision of a square mile section. Since a section is a square with 1-mile sides (thus covering 640 acres), a quarter section would be half of a mile by half of a mile, yielding an area of 160 acres.
Therefore, the correct measurement from the options provided is option 3: 1/2 mile by 1/2 mile. This subdivision was common during the Homestead era, where land was divided for settlement and agricultural purposes. The lands would be further divided or consolidated based on the environmental conditions such as rainfall or the purpose of the land use, like farming or ranching.