Final answer:
After testing each set of lengths against the Pythagorean theorem, none of the options satisfy the condition for forming a right triangle. Therefore, the correct answer is 'D. None of the listed answer choices'.
Step-by-step explanation:
To determine which set of lengths can form a right triangle, we apply the Pythagorean theorem, which states that in a right triangle the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b): a² + b² = c². Let's test each set of lengths given in the options:
- A. 39, 15, and 36 - Check if 15² + 36² = 39²: 225 + 1296 ≠ 1521, so this set can't form a right triangle.
- B. 12, 8, and 4 - Check if 8² + 4² = 12²: 64 + 16 ≠ 144, so this set can't form a right triangle.
- C. 13, 17, and 9 - Check if 9² + 13² = 17²: 81 + 169 = 250 ≠ 289, so this set can't form a right triangle.
None of the listed sets of lengths satisfy the Pythagorean theorem, thus the correct answer is D. None of the listed answer choices.