A rectangular garden has an area of 1500m2 and its perimeter is 200m. Let the breadth of the garden be x metres.
(i) Show that x satisfies the quadratic equation x2−100x+1500=0.
(ii) Without solving the equation obtained in (i), determine whether real dimensions of the garden are possible. Give a reason for your answer.
(iii) Hence find the possible dimensions of the garden, if they exist.