Is a Triangle with Sides 36, 77, and 85 a Right Triangle? Pythagorean Theorem Explained

Learn how to determine if a triangle with sides 36, 77, and 85 is right-angled using the Pythagorean theorem.

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36, 77, and 85 form a right triangle. According to the Pythagorean theorem (a² + b² = c²), if 36² + 77² equals 85², then the triangle is right. Calculating: 36² = 1296, 77² = 5929, and 85² = 7225. Since 1296 + 5929 = 7225, the triangle is indeed right.

FAQs & Answers

  1. How do you verify if a triangle is right-angled using side lengths? You use the Pythagorean theorem: if the sum of the squares of the two shorter sides equals the square of the longest side, the triangle is right-angled.
  2. What is the Pythagorean theorem? It is a mathematical principle stating that in a right triangle, the square of the hypotenuse equals the sum of the squares of the other two sides (a² + b² = c²).
  3. Can sides 36, 77, and 85 form a right triangle? Yes, because 36² + 77² equals 85², confirming it satisfies the Pythagorean theorem.

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For more insights on geometry and math problem-solving, explore our related videos on triangle properties, the Pythagorean theorem applications, and practice problems to strengthen your understanding of right triangles.

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