Question

what type of triangle is 8m, 1m, and 8m
is it unique, not unique, or impossible

Answer 1

To determine the type of triangle formed by the lengths 8m, 1m, and 8m, we can check the triangle inequality theorem. The theorem states that for any triangle with sides \(a\), \(b\), and \(c\):

1. \(a + b > c\)
2. \(a + c > b\)
3. \(b + c > a\)

Let's assign the values:
- \(a = 8m\)
- \(b = 1m\)
- \(c = 8m\)

Now we can check the inequalities:

1. \(8 + 1 > 8\) → \(9 > 8\) (True)
2. \(8 + 8 > 1\) → \(16 > 1\) (True)
3. \(1 + 8 > 8\) → \(9 > 8\) (True)

All three conditions of the triangle inequality are satisfied, which means a triangle can indeed be formed.

Since two sides are equal (8m and 8m), this triangle is classified as an **isosceles triangle**.

In conclusion, the triangle with sides 8m, 1m, and 8m is a unique isosceles triangle.