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To determine if this triangle is a right triangle, let's apply the Pythagorean theorem. In a right triangle, the sum of the squares of the two shorter sides, \(a\) and \(b\), should equal the square of the longest side, \(c\) (the hypotenuse). Here, \(a = 3.2\), \(b = 6\), and \(c = 6.8\).

1. Calculate \(a^2 + b^2\):
   \[
   a^2 + b^2 = 3.2^2 + 6^2 = 10.24 + 36 = 46.24
   \]

2. Calculate \(c^2\):
   \[
   c^2 = 6.8^2 = 46.24
   \]

Since \(a^2 + b^2 = c^2\), the triangle satisfies the Pythagorean theorem, confirming it **is a right triangle**.

Thus:
- The triangle **is** a right triangle.
- The sum of the squares of the shorter sides **equals** the square of the longest side.

Would you like more details, or do you have any questions?

### Related Questions
1. How do you determine if a triangle is right-angled if side lengths aren’t provided?
2. What if one of the side lengths is unknown? How would you calculate it?
3. How does the Pythagorean theorem apply in 3D geometry?
4. What are other properties unique to right triangles?
5. How can you verify if a triangle is right without calculating squares?

### Tip
When verifying if a triangle is a right triangle, always check that the longest side is designated as the hypotenuse \(c\), as only this side should be compared in the Pythagorean theorem.

Is the triangle with side lengths 3.2, 6, and 6.8 a right triangle?

Learn how to determine if a triangle with side lengths 3.2, 6, and 6.8 is a right triangle using the Pythagorean theorem. This geometry problem involves calculating squares of the side lengths to see if the triangle satisfies the conditions of a right triangle. Suitable for students in Grades 6-8.

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