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?

To find the longest line segment in a right rectangular prism, we calculate the space diagonal using the formula:

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

where:

– ( l ) = length = 11.2 cm

– ( w ) = width = 6.6 cm

– ( h ) = height = 6 cm

Now, substituting the values:

1. Calculate ( l^2 ):

[ (11.2)^2 = 125.44 ]

2. Calculate ( w^2 ):

[ (6.6)^2 = 43.56 ]

3. Calculate ( h^2 ):

[ (6)^2 = 36 ]

4. Add these values:

[ 125.44 + 43.56 + 36 = 205 ]

5. Now take the square root:

[ d = sqrt{205} approx 14.3 ]

Therefore, the length of the longest line segment (the space diagonal) is approximately 14.3 cm.