The authorities plan to develop a rectangular lawn whose perimeter exceeds 100m by 20m, while its area is to be exactly 600m2.
a. (i) Translate the perimeter statement into a mathematical expression.
b. (ii) Obtain a quadratic equation in one variable that models the dimensions of the lawn.
c. (iii) Solve the equation and comment on the nature of its solutions.
d. (iv) Based on your result in part (iii), state with reasons whether the proposed lawn can be constructed as specified.