To find the width of the rectangular prism, we can use the formula for the surface area \( S \) of a rectangular prism, which is given by:
\[ S = 2(lw + lh + wh) \]
where:
- \( l \) is the length,
- \( w \) is the width,
- \( h \) is the height.
Given that the surface area \( S = 160 \) cm², the length \( l = 10 \) cm, and the height \( h = 5 \) cm, we can substitute these values into the formula:
\[ 160 = 2(10w + 10 \cdot 5 + 5w) \]
First, simplify the expression inside the parentheses:
\[ 160 = 2(10w + 50 + 5w) \]
Combine the terms:
\[ 160 = 2(15w + 50) \]
Now divide both sides by 2:
\[ 80 = 15w + 50 \]
Next, isolate \( w \) by subtracting 50 from both sides:
\[ 80 - 50 = 15w \] \[ 30 = 15w \]
Now, divide by 15:
\[ w = \frac{30}{15} = 2 \]
Thus, the width of the prism is \( \boxed{2} \) centimeters.
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