The width (\( x \)) of the prism is approximately 45.65 inches.
To find the width (\(x\)) of the prism, we can use the formula for the volume (\(V\)) of a rectangular prism:
\[ V = lwh \]
where:
- \( l \) is the length,
- \( w \) is the width,
- \( h \) is the height.
In this case, the given sides are:
- Length (\( l \)) = 18 inches,
- Width (\( w \)) = \( x \),
- Height (\( h \)) = 14 inches.
The volume (\( V \)) is given as 11,512 in³. So, we can set up the equation:
\[ 11,512 = 18 \times x \times 14 \]
Now, solve for \( x \):
\[ x = \frac{11,512}{18 \times 14} \]
\[ x = \frac{11,512}{252} \]
\[ x \approx 45.65 \text{ inches} \]
Therefore, the width (\( x \)) of the prism is approximately 45.65 inches.