Question

what is the measurement of the longest line segment in a right rectangular prism that is 11.2 centimeters long, 6.6 centimeters wide, and 6 centimeters tall?
the longest line segment is \\(\square\\) cm.
(round to the nearest tenth as needed.)

Explanation:

Step1: Recall the space diagonal formula for a rectangular prism

The space diagonal \( d \) of a rectangular prism with length \( l \), width \( w \), and height \( h \) is given by the formula \( d=\sqrt{l^{2}+w^{2}+h^{2}} \). Here, \( l = 11.2 \) cm, \( w=6.6 \) cm, and \( h = 6 \) cm.

Step2: Calculate \( l^{2}+w^{2}+h^{2} \)

First, calculate each square:

• \( l^{2}=(11.2)^{2}=125.44 \)
• \( w^{2}=(6.6)^{2}=43.56 \)
• \( h^{2}=6^{2} = 36 \)

Then sum them up: \( 125.44+43.56 + 36=125.44+79.56=205 \)

Step3: Take the square root

Now, find the square root of 205: \( d=\sqrt{205}\approx14.3 \) (rounded to the nearest tenth)

Answer:

14.3