To find the missing 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.
We know the following values:
- Length \( l = 6 \) cm,
- Height \( h = 4 \) cm,
- Surface area \( S = 188 \) cm².
We need to find the width \( w \).
Using the surface area formula, we can substitute the known values:
\[ 188 = 2(6w + 6 \cdot 4 + 4w) \]
Calculating \( 6 \cdot 4 \):
\[ 188 = 2(6w + 24 + 4w) \]
Combine like terms:
\[ 188 = 2(10w + 24) \]
Now distribute the 2:
\[ 188 = 20w + 48 \]
Next, isolate \( w \) by subtracting 48 from both sides:
\[ 188 - 48 = 20w \]
\[ 140 = 20w \]
Now, divide both sides by 20:
\[ w = \frac{140}{20} = 7 \]
The missing width of the rectangular prism is \( 7 \) cm.
So, the final answer is:
cm 7