The area of a rectangular floor is 13.5m\(^{2}\). One side is 1.5m longer than the...
The area of a rectangular floor is 13.5m\(^{2}\). One side is 1.5m longer than the other.
(a) Calculate the dimensions of the floor ;
(b) If it costs N250.00 per square metre to carpet the floor and only N2,000.00 is available, what area of the floor can be covered with carpet?
Explanation
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) \(N250 = 1m^{2}\)
\(N2000 = \frac{2000}{250} = 8m^{2}\)
\(\therefore \text{The area of the floor that will be covered by the carpet} = 8m^{2}\)