To find the missing width of a rectangular prism given the length, height, and surface area, you can use the formula for the surface area \( S \) of a rectangular prism:
\[ S = 2(lw + lh + wh) \]
where:
- \( l \) is the length,
- \( w \) is the width,
- \( h \) is the height.
Given:
- Length \( l = 6 \) cm,
- Height \( h = 4 \) cm,
- Surface area \( S = 188 \) cm².
Inserting the known values into the surface area formula gives:
\[ 188 = 2(6w + 6 \cdot 4 + 4w) \]
This simplifies to:
\[ 188 = 2(6w + 24 + 4w) \]
Combining like terms inside the parentheses:
\[ 188 = 2(10w + 24) \]
Dividing both sides by 2:
\[ 94 = 10w + 24 \]
Now, isolating \( w \):
\[ 94 - 24 = 10w \]
Calculating the left side:
\[ 70 = 10w \]
Finally, dividing by 10:
\[ w = 7 , \text{cm} \]
So, the missing width is 7 cm.