To find the missing length of a rectangular prism (also known as a rectangular box), 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:
- Height \( h = 8 \) inches
- Width \( w = 8 \) inches
- Surface Area = 256 in²
We can substitute the given values into the formula:
\[ 256 = 2(l(8) + l(8) + (8)(8)) \]
Simplifying the equation:
\[ 256 = 2(8l + 8l + 64) \] \[ 256 = 2(16l + 64) \] \[ 256 = 32l + 128 \]
Now, we can solve for \( l \):
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Subtract 128 from both sides: \[ 256 - 128 = 32l \] \[ 128 = 32l \]
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Divide both sides by 32: \[ l = \frac{128}{32} = 4 \text{ inches} \]
Thus, the missing length of the rectangular prism is 4 inches.