To find the missing length of a rectangular prism given the height, width, and surface area, we can use the formula for the surface area of a rectangular prism:
\[ \text{Surface Area} = 2(lw + lh + wh) \]
Where \( l \) is the length, \( w \) is the width, and \( h \) is the height. In this case:
- Height (\( h \)) = 7 in
- Width (\( w \)) = 7 in
- Surface Area = 350 in²
We need to find the length (\( l \)).
- Substitute the known values into the surface area formula:
\[ 350 = 2(7 \cdot 7 + 7 \cdot l + 7 \cdot l) \]
- Simplify the equation:
\[ 350 = 2(49 + 7l + 7l) \] \[ 350 = 2(49 + 14l) \] \[ 350 = 98 + 28l \]
- Now, isolate \( l \):
\[ 350 - 98 = 28l \] \[ 252 = 28l \] \[ l = \frac{252}{28} \] \[ l = 9 \]
Thus, the missing length of the rectangular prism is:
\[ \boxed{9} \text{ in.} \]