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)

Answer 1

To find the missing length \( l \) of a rectangular prism when the height \( h \) and width \( w \) are both given, and the surface area \( SA \) is known, we start with the formula for the surface area of a rectangular prism:

\[
SA = 2(hw + hl + wl)
\]

where:
- \( h \) is the height,
- \( w \) is the width,
- \( l \) is the length.

In this problem, we know:
- \( h = 9 \) cm,
- \( w = 9 \) cm,
- \( SA = 432 \) cm\(^2\).

Substituting the known values into the surface area formula:

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

This simplifies to:

\[
432 = 2(81 + 9l + 9l)
\]
\[
432 = 2(81 + 18l)
\]
\[
432 = 162 + 36l
\]

Now, isolate \( l \):

\[
432 - 162 = 36l
\]
\[
270 = 36l
\]
\[
l = \frac{270}{36}
\]
\[
l = 7.5
\]

Thus, the missing length \( l \) of the rectangular prism, rounded to the nearest tenth, is:

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