Final answer:
The area of the rectangular field when X is 45 meters is calculated by multiplying 45 m by 110 m, giving an area of 4950 square meters, which does not match any of the given options.
Step-by-step explanation:
The question asks about calculating the area of a rectangular field using 200 meters of fencing with one side against a barn wall. If one side perpendicular to the barn is X meters long, and X is given as 45 meters, then the total fencing used for the other two sides and the side opposite the barn is 200 - 45 - 45 = 110 meters. This means that the side parallel to the barn is 110 meters long. The area of the rectangular field is then calculated by multiplying the length of the side perpendicular to the barn (X) by the length of the side parallel to the barn.
To find the area when X is 45 meters:
Area = Length × Width
Area = X (perpendicular to the barn) × (Side parallel to the barn)
Area = 45 m × 110 m
Area = 4950 m²
However, this result does not match any of the options given (A: 45 m², B: 50 m², C: 55 m², D: 60 m²). Therefore, those options are incorrect since the calculated area is much larger, and the correct area of the field when X = 45 is not listed in the provided options