Question

A structure is made up of rectangular prisms with a diagonal support bar. A piece is shown.



A figure.Short description, A figure.,Long description,
The figure shows a rectangular prism that is 6 feet wide, 5 feet long, and 4 feet tall. A diagonal support bar goes from the bottom-left corner of the front of the prism to the top-right corner of the back of the prism.


Question
To the nearest hundredth of a foot, how long is the diagonal support bar? Enter the answer in the box.

Response area with 1 text input box
feet

Answer 1

To find the length of the diagonal support bar inside the rectangular prism, we can use the 3-dimensional version of the Pythagorean theorem. The formula for the diagonal \(d\) of a rectangular prism with width \(w\), length \(l\), and height \(h\) is given by:

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

In this case, the dimensions provided are:
- Width \(w = 6\) feet
- Length \(l = 5\) feet
- Height \(h = 4\) feet

Now, plug these values into the formula:

\[
d = \sqrt{6^2 + 5^2 + 4^2}
\]

Calculating the squares:

\[
d = \sqrt{36 + 25 + 16}
\]

Now add the values:

\[
d = \sqrt{77}
\]

Now, calculate the square root of 77:

\[
d \approx 8.775
\]

To the nearest hundredth, the length of the diagonal support bar is:

\[
\boxed{8.78} \text{ feet}
\]