Segments with the lengths 6, 8 and 10 units will form what type of triangle?

hint:

is 6^2 + 8^2 = 10^2 ??

right triangle

To determine the type of triangle formed by segments with lengths 6, 8, and 10 units, we need to apply the triangle inequality theorem. According to this theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

Let's check if this condition is met for the given lengths:
1. The sum of 6 and 8 is 14, which is greater than 10. (6 + 8 = 14 > 10)
2. The sum of 8 and 10 is 18, which is greater than 6. (8 + 10 = 18 > 6)
3. The sum of 6 and 10 is 16, which is greater than 8. (6 + 10 = 16 > 8)

Since all three pairs of sides fulfill the triangle inequality theorem, we can conclude that these segments will form a triangle.

Now, let's determine the type of triangle:
- If all three sides have equal lengths, it is an equilateral triangle.
- If two sides have equal lengths and the third side is different, it is an isosceles triangle.
- If all three sides have different lengths, it is a scalene triangle.

In this case, since the lengths are 6, 8, and 10 units, which are all different, the triangle formed is a scalene triangle.