Answer:
(i) The area of a rectangle is given by the product of its length and width. So, the expression for the area of the given rectangle is:
Area = length × width
Area = (2x - 1)(x + 3)
Area = 2x^2 + 5x - 3
Therefore, the expression for the area of the rectangle in the form of ax^2 + bx + c is 2x^2 + 5x - 3.
(ii) We are given that the area of the rectangle is 294 cm^2. So, we can set the expression for the area equal to 294 and solve for x:
2x^2 + 5x - 3 = 294
2x^2 + 5x - 297 = 0
We can then use the quadratic formula to solve for x:
x = [-b ± sqrt(b^2 - 4ac)] / 2a
x = [-5 ± sqrt(5^2 - 4(2)(-297))] / 4
x = [-5 ± sqrt(4661)] / 4
x ≈ 11.02 or x ≈ -26.77
We discard the negative value of x since it does not make sense in this context. Therefore, the value of x is approximately 11.02.
(iii) We can use the value of x to find the dimensions of the rectangle. The length of the rectangle is (2x - 1) cm, so:
Length = (2x - 1) cm
Length = (2 × 11.02 - 1) cm
Length = 21.04 cm
The width of the rectangle is (x + 3) cm, so:
Width = (x + 3) cm
Width = (11.02 + 3) cm
Width = 14.02 cm
Therefore, the dimensions of the rectangle are 21.04 cm by 14.02 cm.