Arectangle is constructed with its base on the x-axis and two of its vertices on the parabola yequals=196196minus−xsquared2. what are the dimensions of the rectangle with the maximum area? what is that area? let a be the area of the rectangle. what is the objective function that relates a and x? aequals=2 x left parenthesis 196 minus x squared right parenthesis2x196−x2 (type an expression.) the interval of interest of the objective function is left bracket 0 comma 14 right bracket[0,14]. (simplify your answer. type your answer in interval notation.) in the rectangle with the maximum area, the shorter dimension is about 16.1716.17 and the longer dimension is about 130.67130.67. (round to two decimal places as needed.) the maximum area of the rectangle is about 2112.932112.93. (round to two decimal places as neede