Final answer:
The length of AC' in the rectangular prism is found using the three-dimensional Pythagorean theorem, yielding a value of approximately 7.07 units. Since answer options are in whole numbers, we round to 7 units, making the answer D: 7 units.
Step-by-step explanation:
To determine the length of AC' in a 3-dimensional right rectangular prism with dimensions 3×4×5, we must find the diagonal of the prism that stretches from one corner of the base to the opposite corner of the top of the prism (this is often called the space diagonal). Since we are dealing with a right rectangular prism, we can use the Pythagorean theorem in three dimensions.
Let's call the length, width, and height of the prism as a, b, and c, respectively. So in this case, a=3 units, b=4 units, and c=5 units. The length of AC' would be the hypotenuse of the right triangle formed by the sides of length 3, 4, and 5. We use the Pythagorean theorem in three dimensions which is:
Diagonal2 = a2 + b2 + c2
For our prism, this becomes:
AC'2 = 32 + 42 + 52
AC'2 = 9 + 16 + 25
AC'2 = 50
AC' = √50 ≈ 7.07 units
As the options are given in whole numbers, the closest whole number to √50 is 7 units, which makes the answer D: 7 units.