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