Theory question 104
Quadratic EquationsThe area of a rectangular floor is 13.5m2. 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 N2,200.00 is available, what area of the floor can be covered with carpet?
Show the model answer
Model answer
(a) Let the shorter side be x m: x(x + 1.5) = 13.5, so 2x2 + 3x − 27 = 0, (2x + 9)(x − 3) = 0.
x = 3 (a length cannot be negative). The floor is 3 m by 4.5 m.
(b) Area covered = 2200 ÷ 250 = 8.8 m2.
Explanation
Form a quadratic from length × width = area and reject the negative root.