Segments with the lengths of 6, 8, and 10 units will form what type of triangle?
I am pretty sure it will form a scalene obtuse triangle. hope i helped out :)
did you notice that
6^2 + 8^2 = 10^2 ???
mmmh?
To determine the type of triangle formed by segments of lengths 6, 8, and 10 units, we can use 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 segments:
1. Segment of length 6 units
2. Segment of length 8 units
3. Segment of length 10 units
First, let's check the sum of the lengths of segments 1 and 2: 6 + 8 = 14. Since 14 is greater than the length of the third segment (10), the triangle inequality theorem holds for segments 1 and 2.
Next, let's check the sum of the lengths of segments 1 and 3: 6 + 10 = 16. Again, 16 is greater than the length of the second segment (8), so the triangle inequality theorem holds for segments 1 and 3.
Finally, let's check the sum of the lengths of segments 2 and 3: 8 + 10 = 18. Once again, 18 is greater than the length of the first segment (6), so the triangle inequality theorem holds for segments 2 and 3.
Since the triangle inequality theorem holds for all three pairs of segments, the given lengths of 6, 8, and 10 units can form a triangle. To determine the type of triangle, we can use the triangle classification based on side lengths:
- If all three sides are equal, it's an equilateral triangle.
- If two sides are equal, it's an isosceles triangle.
- If all three sides are different, it's a scalene triangle.
In this case, since the lengths of the three given segments are all different (6, 8, and 10 units), the triangle formed would be a scalene triangle.