Can 3, 4, and 5 Form a Right Triangle? Understanding the 3-4-5 Triangle

Discover why the sides 3, 4, and 5 form a right triangle using the Pythagorean theorem in this clear explanation.

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Yes, the numbers 3, 4, and 5 can form a right triangle. In a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. Here, 3² + 4² = 9 + 16 = 25, and 5² = 25, satisfying the Pythagorean theorem. So, a triangle with sides 3, 4, and 5 is indeed a right triangle.

FAQs & Answers

  1. What makes a triangle a right triangle? A triangle is a right triangle if it has one 90-degree angle, and the square of the longest side equals the sum of the squares of the other two sides, following the Pythagorean theorem.
  2. How do I know if the sides 3, 4, and 5 form a right triangle? By applying the Pythagorean theorem: 3² + 4² = 9 + 16 = 25, which equals 5², confirming that the sides form a right triangle.
  3. Are there other sets of numbers like 3, 4, and 5 that form right triangles? Yes, sets of three whole numbers that satisfy the Pythagorean theorem, called Pythagorean triples, such as 5, 12, and 13, also form right triangles.

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