A rectangular garden is fenced on three sides, and the house forms the fourth side of the rectangle.

a. Given that the total length of the fence is 80 m, show that the area, A, of the garden is given by the formula A = y(80 − 2y), where y is the distance from the house to the end of the garden.

b. Given that the area is a maximum for this length of fence, find the dimensions of the enclosed garden, and the area which is enclosed.