To solve this problem, we first need to convert the area into the same units as the perimeter. The area is given in cm^2, which we convert to m^2 because the perimeter is given in meters. To convert cm^2 to m^2, we divide by 10,000 (since 1 m = 100 cm). This gives us an area of 198 m^2.
We now have two equations that we can use to solve for the unknown side of the rectangle:
1. The formula for the area of a rectangle: area = length * width
Substituting the given values into the formula, we get: 198 m^2 = 50 m * width
2. The formula for the perimeter of a rectangle: perimeter = 2 * (length + width)
Substititing the given values into the formula, we get: 62 m = 2 * (50 m + width)
Solving the second equation to find the width, we subtract 50 m from both sides and divide by 2, we get:
width = (62 m - 100 m) / 2 = -19 m
However, a negative width does not make sense in this context. It indicates a calculation mistake which means that the given conditions are incompatible.
Therefore, the given conditions for the problem are not consistent and the problem cannot be solved. So, there's no correct answer among options a, b, c, and d.