3. An open rectangular courtyard measures 28 m in length and 20 m in breadth. A uniform walkway of width x metres is to be built all along the inside edge of the courtyard so that the remaining central rectangular region is covered with grass.
(a) Show that the area A(x) (in m2) of the grassy portion is given by
A(x)=4x2−96x+560.
(b) Determine the value(s) of x for which the grassy area becomes zero.
(c) Explain which of the value(s) obtained in part (b) can actually occur and justify your answer.
(d) Sketch the graph of y=A(x) for suitable values of x, marking clearly the intercepts on both axes.