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.

1 answer

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:

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