The length of a rectangular garden exceeds three times its width by 2\,m. The area of the garden is 99m2.
(i) Taking the width of the garden to be x metres, express the length in terms of x.
(ii) Form an equation in x that represents the area condition and rewrite it in standard quadratic form.
(iii) Factorise the quadratic expression obtained in part (ii) and hence determine the possible numerical values of the width.
(iv) State the corresponding length for each admissible width and justify the rejection of any non-physical solution, if necessary.