Question

what is missing length of rectangle 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 a rectangular prism (also known as a rectangular box), we can use the formula for the surface area of a rectangular prism, which is given by:

\[
\text{Surface Area} = 2(lw + lh + wh)
\]

where:
- \( l \) = length
- \( w \) = width
- \( h \) = height

In this case, the width (\( w \)) and height (\( h \)) are both 8 inches, and the surface area is 256 in². Substituting the known values into the formula gives:

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

Next, simplify the equation:

1. \( 8 \cdot 8 = 64 \)
2. Therefore, the equation becomes:
\[
256 = 2(l \cdot 8 + l \cdot 8 + 64)
\]
\[
256 = 2(16l + 64)
\]
\[
256 = 32l + 128
\]

Now, subtract 128 from both sides:

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

Next, divide both sides by 32 to solve for \( l \):

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

Thus, the missing length of the rectangular prism is:

\[
\boxed{4 \text{ inches}}
\]