To find the missing length of a rectangular prism where the height (h) and width (w) are both 9 cm and the surface area (SA) is 432 cm², we can use the formula for the surface area of a rectangular prism:
\[ SA = 2lw + 2lh + 2wh \]
where:
- \( l \) is the length,
- \( w \) is the width,
- \( h \) is the height.
Given:
- \( h = 9 \) cm
- \( w = 9 \) cm
- \( SA = 432 \) cm²
Substituting the known values into the surface area formula, we have:
\[ 432 = 2l(9) + 2l(9) + 2(9)(9) \]
This simplifies to:
\[ 432 = 18l + 18l + 162 \]
Combining like terms gives:
\[ 432 = 36l + 162 \]
Next, we will isolate \( l \). First, 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 the division gives:
\[ l = 7.5 \]
Thus, the missing length of the rectangular prism is
\[ \boxed{7.5} \text{ cm} \]