Final answer:
The length that will maximize the area is 30 yards.
Therefore, the maximum area is 1800 square yards.
Step-by-step explanation:
To find the length that will maximize the area, we need to determine the value of x that corresponds to the maximum value of the function A = -2(x - 30)^2 + 1800. This function represents a downward-facing parabola, and the maximum value occurs at the vertex. The x-coordinate of the vertex can be found using the formula x = -b / (2a), where a = -2 and b = -60.
Substituting these values into the formula, we get x = -(-60) / (2*-2) = 30 yards.
Therefore, the length that will maximize the area is 30 yards.
To find the maximum area, we substitute the value of x = 30 into the area formula: A = -2(30 - 30)^2 + 1800 = 1800 square yards.
Therefore, the maximum area is 1800 square yards.