Final answer:
The area calculation provided in the question does not match any of the given options, therefore it is not possible to determine the box's height using the available responses without clarification on the correct area formula.
Step-by-step explanation:
The volume V of a rectangular box is given by the formula V = lwh, where l is the length, w is the width, and h is the height of the box. We can calculate the area of the bottom of the box by multiplying the width (w) and the length (l).
Given the width as (3x + 2) and the length as (2 + 3), which simplifies to 5, we have:
- Area of the bottom of the box (A) = (3x + 2) * 5 = 15x + 10 (not in the provided options).
However, since there seems to be an error in the provided question, we'll proceed to find the height using the volume formula (V = lwh). First, let's express the area based on the provided options:
- Area = l * w
- Area = (3x + 2) * 5 = 15x + 10 (not among the given choices)
To find the height (h) given the volume function V(x) = 1223 + 38x2 + 2x - 12:
- We set V(x) = Area * h
- Since none of the areas from the choices match with the calculated area, we cannot accurately determine the height from the given options.
Due to the discrepancy in the area computation, we are not able to select the correct answer from the given options.