Final answer:
To enclose a rectangular field with 40 meters, the best option is to create a square field with each side measuring 10 meters.
Step-by-step explanation:
In this scenario, we are given 40 meters to enclose a rectangular field. Let's analyze each option to determine which one is the best:
Option A: Creating a square field with each side measuring 10 meters would require 4 sides of 10 meters each, totaling 40 meters. This is a viable option, and the area of the square field would be 10 meters multiplied by 10 meters, which equals 100 square meters.
Option B: Making a rectangular field with dimensions of 20 meters by 10 meters. This would require 2 sides of 20 meters and 2 sides of 10 meters, totaling 60 meters. Therefore, this option is not possible.
Option C: Forming a circular field with a radius of 20 meters. The circumference of a circle is given by the formula C = 2πr. Plugging in the values, we get C = 2 x 3.14 x 20 = 125.6 meters. This option is not possible since the circumference exceeds the available 40 meters.
Option D: Using the 40 meters to create a triangular field. Let's assume that the length of the third side is x meters. The sum of the three sides of a triangle must equal the perimeter of the field, so we have 80 + 105 + x = 40. Solving for x, we get x = 40 - 80 - 105 = -145. This amount is not physically possible, so this option is not valid.
Based on our analysis, the best option is Option A - creating a square field with each side measuring 10 meters.