To find the longest line segment that can be drawn in a right rectangular prism (also called a box), we need to calculate the length of the space diagonal of the prism. The formula to find the length of the space diagonal \( d \) of a rectangular prism with dimensions \( l \) (length), \( w \) (width), and \( h \) (height) is:
\[ d = \sqrt{l^2 + w^2 + h^2} \]
In this case, the dimensions are:
- Length \( l = 12 , \text{cm} \)
- Width \( w = 11 , \text{cm} \)
- Height \( h = 8 , \text{cm} \)
Plugging in the dimensions into the formula:
\[ d = \sqrt{(12)^2 + (11)^2 + (8)^2} \]
Calculating each term:
\[ (12)^2 = 144 \] \[ (11)^2 = 121 \] \[ (8)^2 = 64 \]
Now, add these values together:
\[ 144 + 121 + 64 = 329 \]
Now, take the square root:
\[ d = \sqrt{329} \]
Calculating the square root:
\[ d \approx 18.14 , \text{cm} \]
Therefore, the longest line segment that can be drawn in the right rectangular prism is approximately 18.14 cm.