Question

can a triangle be formed with these lengths? 2cm, 2cm, 3cm

Answer 1

To determine if a triangle can be formed with the given lengths, we can use the triangle inequality theorem. According to this theorem, for any triangle with sides of lengths \(a\), \(b\), and \(c\), the following conditions must hold true:

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

In your case, the side lengths are 2 cm, 2 cm, and 3 cm. Let's denote these as \(a = 2\) cm, \(b = 2\) cm, and \(c = 3\) cm, and check the inequalities:

1. \(a + b > c\) → \(2 + 2 > 3\) → \(4 > 3\) (True)
2. \(a + c > b\) → \(2 + 3 > 2\) → \(5 > 2\) (True)
3. \(b + c > a\) → \(2 + 3 > 2\) → \(5 > 2\) (True)

Since all three conditions are satisfied, a triangle can indeed be formed with the lengths of 2 cm, 2 cm, and 3 cm.