Question

A triangle can be formed with side measures of 4.6, 2.7, and 1.9. Enter 1 for “true” or 2 for “false”.(1 point)
Remaining Attempts : 3

Answer 1

To determine if a triangle can be formed with the given side lengths, we can use the triangle inequality theorem. This theorem states that for any triangle with sides \( a \), \( b \), and \( c \), the following conditions must be met:

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

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

Now we will check the triangle 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 the third condition does not hold (it is not greater, it is equal), the given side lengths cannot form a triangle.

Therefore, the answer is **2 for false**.