Question

type the correct answer in the box. use numerals instead of words.
what is the length of the diagonal shown in the rectangular prism? round your answer to the nearest tenth.
7 ft
5 ft
4 ft
ft

Explanation:

Step1: Recall the formula for the space diagonal of a rectangular prism.

The formula for the length of the space diagonal \( d \) of a rectangular prism with length \( l \), width \( w \), and height \( h \) is \( d = \sqrt{l^2 + w^2 + h^2} \). Here, \( l = 7 \) ft, \( w = 4 \) ft, and \( h = 5 \) ft.

Step2: Substitute the values into the formula.

First, calculate the squares of each dimension:
\( l^2 = 7^2 = 49 \)
\( w^2 = 4^2 = 16 \)
\( h^2 = 5^2 = 25 \)

Then, sum these squares:
\( 49 + 16 + 25 = 90 \)

Step3: Take the square root of the sum.

\( d = \sqrt{90} \approx 9.5 \) (rounded to the nearest tenth)

Answer:

9.5