To find the missing length \( l \) of the rectangular prism, we can use the formula for the surface area of a rectangular prism, which is given by:
\[ SA = 2(lw + lh + wh) \]
where \( l \) is the length, \( w \) is the width, and \( h \) is the height. In this case, we know:
- Width \( w = 9 \) cm
- Height \( h = 9 \) cm
- Surface Area \( SA = 432 \) cm²
We can substitute the values into the surface area formula:
\[ 432 = 2(l \cdot 9 + l \cdot 9 + 9 \cdot 9) \]
Simplifying the inside of the parentheses:
\[ 432 = 2(9l + 9l + 81) \] \[ 432 = 2(18l + 81) \] \[ 432 = 36l + 162 \]
Next, we will isolate \( l \):
\[ 432 - 162 = 36l \] \[ 270 = 36l \] \[ l = \frac{270}{36} \] \[ l = 7.5 \]
Thus, the missing length \( l \) of the rectangular prism is:
\[ \boxed{7.5} , \text{cm} \]