A rectangular park is required to have an area of 400m2, while a contractor claims that its perimeter is 90m.
(i) Derive an equation in one variable that represents the above information.
(ii) Without solving the equation, calculate its discriminant.
(iii) What does the value obtained in part (ii) tell you about the nature of the roots of the equation?
(iv) Using your conclusion from part (iii), explain whether a rectangle with the stated area and perimeter can actually exist. Give reasons.