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) \(N250 = 1m^{2}\)
\(N2000 = \frac{2000}{250} = 8m^{2}\)
\(\therefore \text{The area of the floor that will be covered by the carpet} = 8m^{2}\)