Consider all rectangles with area 144 cm2. Using the steps below, find the dimensions _ cm x y cm of the rectangle with the shortest perimeter. (a) Find the perimeter P of the rectangle in terms of the length a cm of the rectangle. Enter your answer for P(x) as a function of x below. You should launch the equation editor for easy entry. sin (a) ? (b) What happens to the side of length z and as the side of the length y changes? The length a gets shorter while the length y gets shorter. The length a gets longer while the length y gets shorter. The length a gets longer while the length y gets longer. The length a gets shorter while the length y gets longer. (c) What are the possible values of ? You should include degenerate rectangles in your considerations whenever they still make sense in the problem? Find in your answer as an inequality below. Enter infinity for oo and -infinity for -Do. Click for List Click for List (d) Find the value of a that minimizes the perimeter of the rectangle with area 144 cm2. Number cm. (e) What is the minimal length of the perimater of the rectangle with area 144 cm?? Number cm