The triangle with side lengths of 6, 8, and 10 is a right triangle. To determine if a triangle is a right triangle, we can apply the Pythagorean theorem, which states that 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 lengths of the other two sides.
In this case, we can label the sides as follows: 6 and 8 are the two shorter sides, and 10 is the longest side, which we will consider as the hypotenuse. Now, we can check if it satisfies the Pythagorean theorem:
- Hypotenuse² = 10² = 100
- Other sides² = 6² + 8² = 36 + 64 = 100
Since both sides of the equation are equal (100 = 100), we can conclude that the triangle is indeed a right triangle. Therefore, the triangle with side lengths of 6, 8, and 10 not only forms a valid triangle but also has a right angle between the two shorter sides.