Question

Side lengths of 26 meters, 50 meters, and 60 meters will form a triangle?

true pr false

Answer 1

To determine whether the side lengths of 26 meters, 50 meters, and 60 meters can form a triangle, we can use the triangle inequality theorem. The theorem states that for any triangle with sides of lengths \(a\), \(b\), and \(c\), the following conditions must be met:

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

Let's assign the side lengths as follows:
- \(a = 26\)
- \(b = 50\)
- \(c = 60\)

Now we check the triangle inequalities:

1. \(a + b > c\):
\(26 + 50 > 60\)
\(76 > 60\) (True)

2. \(a + c > b\):
\(26 + 60 > 50\)
\(86 > 50\) (True)

3. \(b + c > a\):
\(50 + 60 > 26\)
\(110 > 26\) (True)

Since all three conditions are satisfied, the side lengths of 26 meters, 50 meters, and 60 meters can indeed form a triangle.

So the answer is **true**.