To find the length of \( d \) in the three-dimensional rectangular prism given the dimensions, we can use the 3D distance formula. The length \( d \) is the space diagonal of the rectangular prism, which can be calculated using the formula:
\[ d = \sqrt{l^2 + w^2 + h^2} \]
Given the dimensions:
- \( l = 30 \) in
- \( w = 20 \) in
- \( h = 18 \) in
We can substitute these values into the formula:
\[ d = \sqrt{(30)^2 + (20)^2 + (18)^2} \]
Calculating each square:
\[ (30)^2 = 900, \] \[ (20)^2 = 400, \] \[ (18)^2 = 324 \]
Adding these together:
\[ 900 + 400 + 324 = 1624 \]
Now, take the square root of \( 1624 \):
\[ d = \sqrt{1624} \approx 40.31 \text{ in} \]
Rounding to the nearest tenth, we find:
\[ d \approx 40.3 \text{ in} \]
Thus, the length of \( d \) is approximately 40.3 in.