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)

Answer 1

To determine if a triangle can be formed with side measures of 4.6, 2.7, and 1.9, 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 check the 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)

The third inequality is not true, as 4.6 is not greater than 4.6. Therefore, a triangle cannot be formed with these side lengths.

The answer is 2 (false).