To find the length \( d \), we can use the Pythagorean theorem in a three-dimensional context. The formula for the diagonal \( d \) of a rectangular box 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, summing these values:
\[ 900 + 400 + 324 = 1624 \]
Now, taking 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.
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