Is a Right Triangle with Sides 6cm, 8cm, and 10cm Possible?

Discover if a triangle with sides 6cm, 8cm, and 10cm can form a right triangle based on the Pythagorean theorem.

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No, a right triangle with sides 6cm, 10cm, and 8cm cannot be formed. According to the Pythagorean theorem, the sum of the squares of the two shorter sides must equal the square of the longest side. Here, 6² + 8² = 36 + 64 = 100, which does not equal 10² = 100. Therefore, this set of sides does not satisfy the condition for a right triangle.

FAQs & Answers

  1. What is the Pythagorean theorem? The Pythagorean theorem 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.
  2. How do you check if a triangle is a right triangle? To check if a triangle is a right triangle, use the Pythagorean theorem: a² + b² = c², where c is the longest side.
  3. Can any three sides form a triangle? Not always; the lengths of the sides must satisfy the triangle inequality theorem.
  4. What are the different types of triangles? Triangles can be classified as scalene, isosceles, or equilateral based on the length of their sides, and as acute, right, or obtuse based on their angles.

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