A lifeguard needs to rope off a rectangular swimming area in front of Long Lake Beach, using 800 yd of rope and floats. What dimensions of the rectangle will maximize the area? What is the maximum area? (Note that the shoreline is one side of the rectangle.) Let x be the length of a side of the rectangle perpendicular to the shoreline. Write the objective function for the area in terms of x. A(x)= (Type an expression using x as the variable.). The length of the shorter side of the rectangular region is The length of the longer side of the rectangular region is The maximum area of the rectangular region is