【Answer】: 1. 238 cm²
【Explanation】: 1. The question is asking for the surface area (SA) of a rectangular prism. The formula for the surface area of a rectangular prism is given by:
\[ SA = 2lw + 2lh + 2wh \]
where \( l \) is the length, \( w \) is the width, and \( h \) is the height of the prism.
2. In this question, the values of \( l \), \( w \), and \( h \) are given as 3 cm, 5 cm, and 4 cm respectively.
3. Substituting these values into the formula, we get:
\[ SA = 2(3 \, \text{cm})(5 \, \text{cm}) + 2(3 \, \text{cm})(4 \, \text{cm}) + 2(5 \, \text{cm})(4 \, \text{cm}) \]
4. Calculating each term separately, we get:
\[ SA = 2(15 \, \text{cm}^2) + 2(12 \, \text{cm}^2) + 2(20 \, \text{cm}^2) \]
\[ SA = 30 \, \text{cm}^2 + 24 \, \text{cm}^2 + 40 \, \text{cm}^2 \]
5. Adding these values together, we get:
\[ SA = 94 \, \text{cm}^2 \]
6. However, the question also mentions a value of \( x = 17 \, \text{cm} \). It's unclear how this value relates to the prism, as it's not used in the formula for the surface area of a rectangular prism. Therefore, it's possible that there might be a missing context or additional information required to understand the significance of \( x \) in this question.
7. Without the context or additional information regarding \( x \), we can only provide the surface area based on the given dimensions of the prism, which is \( 94 \, \text{cm}^2 \).
8. However, if we assume that \( x \) represents an additional dimension or a different prism altogether, the surface area calculation would be different. In that case, the question would be incomplete or unclear, and thus, the conditions given in the question would be insufficient to provide a definitive answer.
9. In summary, based on the given information and the formula for the surface area of a rectangular prism, the surface area is \( 94 \, \text{cm}^2 \). However, the presence of \( x = 17 \, \text{cm} \) without further context makes the question ambiguous.
