Question

Given l=30 in. , w=20 in. , h=18 in. , and x=36.1 in. , find the length of d . Round the answer to the nearest tenth.

Answer 1

To find the length \( d \), we'll assume you are referring to a diagonal in a bounding box defined by the given dimensions \( l \), \( w \), and \( h \). The length of the diagonal \( d \) of a rectangular prism can be calculated using the formula:

\[
d = \sqrt{l^2 + w^2 + h^2}
\]

Given:
- \( l = 30 \) inches
- \( w = 20 \) inches
- \( h = 18 \) inches

Substituting these values into the formula, we have:

\[
d = \sqrt{30^2 + 20^2 + 18^2}
\]

Calculating each term:

\[
30^2 = 900
\]
\[
20^2 = 400
\]
\[
18^2 = 324
\]

Now sum these values:

\[
900 + 400 + 324 = 1624
\]

Now take the square root:

\[
d = \sqrt{1624}
\]

Using a calculator, we find:

\[
d \approx 40.3
\]

Thus, the length of \( d \) rounded to the nearest tenth is:

\[
\boxed{40.3} \text{ inches}
\]