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. 4 ft 5 ft 7 ft

Explanation:

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

The formula for 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, \( l = 5 \) ft, \( w = 4 \) ft, and \( h = 7 \) ft.

Step2: Substitute the values into the formula.

Substitute \( l = 5 \), \( w = 4 \), and \( h = 7 \) into the formula: \( d = \sqrt{5^2 + 4^2 + 7^2} \). Calculate the squares: \( 5^2 = 25 \), \( 4^2 = 16 \), \( 7^2 = 49 \). Then sum them: \( 25 + 16 + 49 = 90 \). So, \( d = \sqrt{90} \).

Step3: Simplify and round.

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

Answer:

9.5