To find the length of the diagonal \( d \) in a rectangular prism, we can use the 3D distance formula. The formula to find the length of the diagonal \( d \) of a rectangular prism with length \( l \), width \( w \), and height \( h \) is given by:
\[ d = \sqrt{l^2 + w^2 + h^2} \]
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 term:
\[ (30)^2 = 900 \] \[ (20)^2 = 400 \] \[ (18)^2 = 324 \]
Now, add them together:
\[ 900 + 400 + 324 = 1624 \]
Now find the square root:
\[ d = \sqrt{1624} \approx 40.249 \]
Rounding to the nearest tenth:
\[ d \approx 40.2 \text{ in} \]
Thus, the length of \( d \) is approximately 40.2 in.