Question

can a triangle be formed with the lengths 1cm, 2cm, and 4cm?

Answer 1

To determine whether a triangle can be formed with side lengths of 1 cm, 2 cm, and 4 cm, we can use the triangle inequality theorem. This theorem states that for any triangle with side lengths \(a\), \(b\), and \(c\), the following conditions must hold:

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

Let's apply this to the given lengths \(1\) cm, \(2\) cm, and \(4\) cm.

1. \(1 + 2 > 4\) → \(3 > 4\) (False)
2. \(1 + 4 > 2\) → \(5 > 2\) (True)
3. \(2 + 4 > 1\) → \(6 > 1\) (True)

Since the first condition is false, the lengths 1 cm, 2 cm, and 4 cm cannot form a triangle.