A rectangular field is 32 m long and 18 m wide. It is to be enlarged by adding a path of uniform width x metres all around the outside so that the total area of the field together with the path becomes 1 176 m².
(a) Form an equation in x representing the new total area.
(b) Rewrite the equation obtained in part (a) by first extracting the greatest common factor and then reduce it to a quadratic equation with leading coefficient 1.
(c) Factorise the quadratic equation obtained in part (b).
(d) Hence find the width of the path.
(e) Calculate the percentage increase in the area of the field after the path is added.