Is a Triangle with Sides 9, 12, and 15 a Right Triangle? Pythagorean Theorem Explained

Learn how to check if a triangle with sides 9, 12, and 15 is right-angled using the Pythagorean theorem in this quick Q&A.

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No, 9, 12, and 15 do not form a right triangle. To check, use the Pythagorean theorem (a² + b² = c²): 9² + 12² = 81 + 144 = 225, but 15² = 225. Therefore, 81 + 144 ≠ 225, so this is not a right triangle.

FAQs & Answers

  1. How do I know if a triangle is a right triangle? You can verify if a triangle is right-angled by using the Pythagorean theorem: if the square of the longest side equals the sum of the squares of the other two sides, it is a right triangle.
  2. Is a triangle with sides 9, 12, and 15 a right triangle? Yes, since 9² + 12² equals 81 + 144 which is 225, and 15² is 225, they satisfy the Pythagorean theorem, so this is a right triangle.
  3. What is the Pythagorean theorem? The Pythagorean theorem states that in a right triangle, the square of the hypotenuse (longest side) equals the sum of the squares of the other two sides.

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