Final answer:
To find the length of the prism, divide the area of the base (2x^2 + 4x - 6) by the width (2x - 2). Simplifying the division gives us the length in terms of x, which should match one of the answer choices, but it seems there is a discrepancy as the correct length (x + 3) is not listed among the options.
Step-by-step explanation:
The width of the prism is given as (2x - 2) ft and its height is (x + 6) ft. The area of the base of the prism is given as (2x2 + 4x - 6) ft2. To find the length of the prism, we would normally use the area formula for the base of the prism, which is Area = Length * Width. However, in this problem, we are provided with the area and the width, and we need to solve for the Length.
To find the length of the prism, we can set up the equation (Length) * (Width) = Area of Base, where the Width is (2x - 2) and the Area of Base is (2x2 + 4x - 6). We then solve this equation:
Length * (2x - 2) = 2x2 + 4x - 6
We can divide both sides of the equation by the width (2x - 2) to find the Length:
Length = (2x2 + 4x - 6) / (2x - 2)
When we simplify the right side of the equation by dividing, we find that the only expression for Length that matches one of the provided answer choices is (x + 3). However, this option is not listed among the given choices (a) through (d), which suggests that there might be either a mistake in the formation of the question or in the provided answer choices. A recalculation of the division or a review of the given options may be required to ensure accuracy.