Question

Question
What is the missing length of a rectangular prism where the height and width are both 9 cm and the surface area is 432 cm2
? Express your answer as a decimal rounded to the nearest tenth.(1 point)
cm

Answer 1

To find the missing length of the rectangular prism, we will use the formula for the surface area of a rectangular prism:

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

where \( l \) is the length, \( w \) is the width, and \( h \) is the height. In this case, we know that:

- \( w = 9 \) cm (width)
- \( h = 9 \) cm (height)
- Surface Area = 432 cm²

Plugging these values into the surface area formula, we have:

\[
432 = 2(l \cdot 9) + 2(l \cdot 9) + 2(9 \cdot 9)
\]

Simplifying the equation step by step:

1. Calculate \( 2(9 \cdot 9) \):

\[
2(81) = 162
\]

2. Substitute back into the equation:

\[
432 = 18l + 18l + 162
\]

Combine like terms:

\[
432 = 36l + 162
\]

3. Subtract 162 from both sides:

\[
432 - 162 = 36l
\]
\[
270 = 36l
\]

4. Now, divide both sides by 36 to solve for \( l \):

\[
l = \frac{270}{36}
\]

Calculating this gives:

\[
l = 7.5
\]

Thus, the missing length of the rectangular prism, rounded to the nearest tenth, is:

\[
\boxed{7.5} \text{ cm}
\]