Question

What is the missing length of a rectangular prism where the height and width are both "7 in." and the surface area is 350 in.²?(1 point)

Answer 1

To find the missing length of a rectangular prism given the height, width, and surface area, 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. In this case:

- Height (\( h \)) = 7 in
- Width (\( w \)) = 7 in
- Surface Area = 350 in²

We need to find the length (\( l \)).

1. Substitute the known values into the surface area formula:

\[
350 = 2(7 \cdot 7 + 7 \cdot l + 7 \cdot l)
\]

2. Simplify the equation:

\[
350 = 2(49 + 7l + 7l)
\]
\[
350 = 2(49 + 14l)
\]
\[
350 = 98 + 28l
\]

3. Now, isolate \( l \):

\[
350 - 98 = 28l
\]
\[
252 = 28l
\]
\[
l = \frac{252}{28}
\]
\[
l = 9
\]

Thus, the missing length of the rectangular prism is:

\[
\boxed{9} \text{ in.}
\]