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)
c

Answer 1

To find the missing length of the rectangular prism, we can 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. Given that both the width \( w \) and the height \( h \) are 9 cm, we can plug these values into the formula. Let \( l \) be the missing length we are trying to find.

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

This simplifies to:

\[
432 = 2(9l) + 2(9l) + 2(81)
\]

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

\[
432 = 36l + 162
\]

Next, we subtract 162 from both sides:

\[
432 - 162 = 36l
\]

\[
270 = 36l
\]

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

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

Calculating this gives:

\[
l = 7.5
\]

Thus, the missing length is

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