Question

What is missing length of rectangular prism if height and width are both 8 inches. And surface area is 256 in^2. Proper units

Make the explanation simple

Answer 1

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).

1. Substitute the known values into the formula:

\[
256 = 2(l \cdot 8 + l \cdot 8 + 8 \cdot 8)
\]

2. Simplify the equation:

\[
256 = 2(8l + 8l + 64)
\]
\[
256 = 2(16l + 64)
\]
\[
256 = 32l + 128
\]

3. Now, isolate \( l \):

\[
256 - 128 = 32l
\]
\[
128 = 32l
\]

4. Finally, divide to find \( l \):

\[
l = \frac{128}{32} = 4
\]

So, the missing length of the rectangular prism is **4 inches**.