Let's analyze each set of numbers using the Pythagorean theorem, which states that for a right triangle with sides $a$, $b$, and hypotenuse $c$:

$a^2 + b^2 = c^2$

Set A: $6, 12, 15$

• Assume the largest number, $15$, is the hypotenuse.
• Compute:

$6^2 + 12^2 = 36 + 144 = 180$

$15^2 = 225$

Since $180 \neq 225$, the numbers do not represent a right triangle.

Set B: $5, 12, 13$

• Assume the largest number, $13$, is the hypotenuse.
• Compute:

$5^2 + 12^2 = 25 + 144 = 169$

$13^2 = 169$

Since $169 = 169$, the numbers do represent a right triangle.

Conclusion:

• Set A (6, 12, 15): ❌ Not a right triangle.
• Set B (5, 12, 13): ✔ Right triangle.

Would you like further details or have any questions?

Here are 5 related questions to expand on the topic:

1. How do you determine the hypotenuse in a given set of numbers?
2. Can the Pythagorean theorem be used for non-right triangles?
3. What are Pythagorean triples, and how can they be generated?
4. How does the Pythagorean theorem apply in real-world problems?
5. What is the converse of the Pythagorean theorem?

Tip: A quick way to check if three numbers form a right triangle is to identify if they belong to a known Pythagorean triple such as (3,4,5) or (5,12,13).