Question

Wut is missing length of rectangular prism ig height and width r 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:

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

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 \( l \):

1. Subtract 128 from both sides:
\[
256 - 128 = 32l
\]
\[
128 = 32l
\]

2. Divide both sides by 32:
\[
l = \frac{128}{32} = 4 \text{ inches}
\]

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