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

Answer 1

To find the missing length of the 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 \( S \) of a rectangular prism:

\[
S = 2(lw + lh + wh)
\]

where:
- \( l \) is the length,
- \( w \) is the width,
- \( h \) is the height.

In this case, we know:
- \( h = 8 \) inches
- \( w = 8 \) inches
- \( S = 256 \) square inches

Substituting the known values into the surface area formula:

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

This simplifies to:

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

Next, we isolate the term with \( l \):

\[
256 - 128 = 32l
\]
\[
128 = 32l
\]
\[
l = \frac{128}{32}
\]
\[
l = 4 \text{ inches}
\]

Thus, the missing length of the rectangular prism is \( 4 \) inches.