To find the surface area of a rectangular prism with dimensions [tex]\(x\)[/tex] units, [tex]\(2x\)[/tex] units, and [tex]\(x + 8\)[/tex] units, let's follow these steps:
1. Identify the dimensions:
- Length ([tex]\(l\)[/tex]): [tex]\(x\)[/tex] units
- Width ([tex]\(w\)[/tex]): [tex]\(2x\)[/tex] units
- Height ([tex]\(h\)[/tex]): [tex]\(x + 8\)[/tex] units
2. Surface area of a rectangular prism:
The formula for the surface area ([tex]\(SA\)[/tex]) of a rectangular prism is:
[tex]\[
SA = 2(lw + lh + wh)
\][/tex]
3. Plug in the dimensions into the formula:
[tex]\[
SA = 2(x \cdot 2x + x \cdot (x + 8) + 2x \cdot (x + 8))
\][/tex]
4. Calculate each part of the expression inside the parentheses:
- [tex]\(lw = x \cdot 2x = 2x^2\)[/tex]
- [tex]\(lh = x \cdot (x + 8) = x^2 + 8x\)[/tex]
- [tex]\(wh = 2x \cdot (x + 8) = 2x^2 + 16x\)[/tex]
5. Add these parts together:
[tex]\[
2x^2 + x^2 + 8x + 2x^2 + 16x = 5x^2 + 24x
\][/tex]
6. Multiplying by 2 to get the total surface area:
[tex]\[
SA = 2 \cdot (5x^2 + 24x) = 10x^2 + 48x
\][/tex]
Thus, the expression that represents the surface area of the prism is:
[tex]\[
10x^2 + 48x \text{ square units}
\][/tex]
Therefore, the correct answer is:
[tex]\[ \boxed{10 x^2 + 48 x \text{ square units}} \][/tex]
