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:
- Calculate \( 2(9 \cdot 9) \):
\[ 2(81) = 162 \]
- Substitute back into the equation:
\[ 432 = 18l + 18l + 162 \]
Combine like terms:
\[ 432 = 36l + 162 \]
- 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 of the rectangular prism, rounded to the nearest tenth, is:
\[ \boxed{7.5} \text{ cm} \]