Question

Which of the following three sets of lengths could be used to form a right triangle?

A. 39, 15, and 36
B. 12, 8, and 4
C. 13, 17, and 9
D. None of the listed answer choices

Answer 1

The three sets of lengths that could be used to form a right triangle are A. 39, 15, and 36; B. 12, 8, and 4; C. 13, 17, and 9. However, none of the listed answer choices can form a right triangle.

Step-by-step explanation:

The three sets of lengths that could be used to form a right triangle are:

1. A. 39, 15, and 36
2. B. 12, 8, and 4
3. C. 13, 17, and 9

To determine if these sets of lengths can form a right triangle, we can apply the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.

For example, for set A, we have:
a² + b² = c²
39² + 15² = 36²
1521 + 225 = 1296
This equation is not true, so set A cannot form a right triangle.

Similarly, we can check sets B and C using the same method.

Therefore, the correct answer is D. None of the listed answer choices.