Length of the interior diagonal of the right rectangular prism.

To find the length of the interior diagonal of a right rectangular prism, you can use the formula:

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

where ( l ) is the length, ( w ) is the width, and ( h ) is the height of the prism. In this case:

– ( l = 5 ) cm

– ( w = 3 ) cm

– ( h = 2 ) cm

Now, we can calculate the diagonal:

1. Square each dimension:

– ( l^2 = 5^2 = 25 )

– ( w^2 = 3^2 = 9 )

– ( h^2 = 2^2 = 4 )

2. Add these values together:

– ( 25 + 9 + 4 = 38 )

3. Take the square root of the sum:

– ( d = sqrt{38} approx 6.16 )

So, the length of the interior diagonal of the prism is approximately ( 6.16 ) cm, which corresponds to option A.

Answer: A) 6.16