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 N250.0...
Question 1 Report
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?
Answer Details
(a) Dimensions. Let the shorter side be \(x\) m; the longer side is \(x + 1.5\) m. The area is 13.5 m²:
\[x(x + 1.5) = 13.5 \Rightarrow x^2 + 1.5x - 13.5 = 0.\]
Multiply through by 2: \(2x^2 + 3x - 27 = 0\), which factorises as \((2x + 9)(x - 3) = 0\).
Taking the positive root, \(x = 3\). So the dimensions are
\[3\text{ m by }4.5\text{ m}.\]
(b) Area that can be carpeted. At N250.00 per square metre with N2,000.00 available:
\[\text{Area} = \frac{2000}{250} = 8\text{ m}^2.\]
So 8 m² of the floor can be covered (the floor is 13.5 m², so it cannot all be carpeted).
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