Final answer:
Another rectangular field with the same perimeter of 400 meters but a smaller area would have dimensions such as 130 meters long and 70 meters wide, resulting in an area of 9100 square meters, less than the original 9375 square meters.
Step-by-step explanation:
To find the length and width of another rectangular field with the same perimeter but a smaller area than the original field that is 125 meters long and 75 meters wide, we first calculate the perimeter of the original field. The formula for the perimeter of a rectangle is P = 2(l + w), where P is perimeter, l is length, and w is width.
The perimeter of the original field is 2(125 + 75) meters, which equals 400 meters. To have the same perimeter but a smaller area, we need to change the dimensions in such a way that when we add the new length and width, the sum is half the perimeter (200 meters), but the product (length times width) is less than the product of the original dimensions.
For example, a rectangle that is 130 meters long and 70 meters wide has a perimeter that equals 2(130 + 70) = 400 meters, just like the original field, but the area is smaller because 130 × 70 = 9100 square meters, which is less than 125 × 75 = 9375 square meters.
Therefore, the dimensions of another rectangular field with the same perimeter (400 meters) but a smaller area (9100 square meters) are 130 meters long and 70 meters wide.