Let one of the sides be x metres. The other is (x + 1.5) metres. (a) \(Area = Length \times breadth\) \(x(x + 1.5) = 13.5\) \(x^{2} + 1.5x = 13.5 \implies x^{2} + 1.5x - 13.5 = 0\) \(x^{2} + 4.5x - 3x - 13.5 = 0 \implies x(x + 4.5) - 3(x + 4.5) = 0\) \((x - 3)(x + 4.5) = 0 \implies x = 3 ; x = -4.5\) Since x cannot be negative, therefore x = 3m. The longer side = (3 + 1.5) = 4.5m (b) \(N250 = 1m^{2}\) \(N2000 = \frac{2000}{250} = 8m^{2}\) \(\therefore \text{The area of the floor that will be covered by the carpet} = 8m^{2}\)