Step 1 :The problem is asking for a function that gives the area of the field in terms of x. The area of a rectangle is given by the formula length * width. In this case, the length is x and the width is the remaining fencing after subtracting the length of x from the total fencing of 120 meters. Since there are two sides of the rectangle that are the same length (x), the width would be 120 - 2x.
Step 2 :Therefore, the area function would be \(A(x) = x * (120 - 2x)\).
Step 3 :Final Answer: The function that gives the area of the field in terms of \(x\) is \(\boxed{A(x) = x * (120 - 2x)}\).