To find the missing width of a rectangular prism, we can use the formula for the surface area of a rectangular prism:
\[ \text{Surface Area} = 2(lw + lh + wh) \]
where \( l \) is the length, \( w \) is the width, and \( h \) is the height.
Given:
- Length \( l = 6 , \text{cm} \)
- Height \( h = 4 , \text{cm} \)
- Surface Area = 188 cm²
We can substitute the known values into the surface area formula:
\[ 188 = 2(6w + 6 \cdot 4 + 4w) \]
Calculating the constant parts first:
\[ 188 = 2(6w + 24 + 4w) \]
Combine the terms inside the parentheses:
\[ 188 = 2(10w + 24) \]
Now divide both sides by 2:
\[ 94 = 10w + 24 \]
Next, subtract 24 from both sides:
\[ 94 - 24 = 10w \] \[ 70 = 10w \]
Now, divide by 10:
\[ w = \frac{70}{10} = 7 , \text{cm} \]
So, the missing width of the rectangular prism is:
\[ \boxed{7 , \text{cm}} \]