To find the missing length of a rectangular prism when the height and width are both 8 inches and the surface area is 256 square inches, 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 (8 inches),
- \( h \) is the height (8 inches).
- Substitute the known values into the formula:
\[ 256 = 2(l \cdot 8 + l \cdot 8 + 8 \cdot 8) \]
- Simplify the equation:
\[ 256 = 2(8l + 8l + 64) \] \[ 256 = 2(16l + 64) \] \[ 256 = 32l + 128 \]
- Now, isolate \( l \):
\[ 256 - 128 = 32l \] \[ 128 = 32l \]
- Finally, divide to find \( l \):
\[ l = \frac{128}{32} = 4 \]
So, the missing length of the rectangular prism is 4 inches.