Question

triangle can be formed with sides 4.6, 2.7 and 1.9 true or false

Answer 1

To determine if a triangle can be formed with the given sides, we can use the triangle inequality theorem. This theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

Let's denote the sides as:
- \( a = 4.6 \)
- \( b = 2.7 \)
- \( c = 1.9 \)

We need to check the following inequalities:

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

Now, let's evaluate these inequalities:

1. \( 4.6 + 2.7 > 1.9 \)
- \( 7.3 > 1.9 \) (True)

2. \( 4.6 + 1.9 > 2.7 \)
- \( 6.5 > 2.7 \) (True)

3. \( 2.7 + 1.9 > 4.6 \)
- \( 4.6 > 4.6 \) (False)

Since one of the inequalities (the third one) is not satisfied, a triangle cannot be formed with the sides 4.6, 2.7, and 1.9.

Thus, the answer is **false**.