Question

Using the Triangle Inequality Theorem (see picture above), determine the length of the third side of the triangle.



(2 points)
Responses

Side x equals 1 m
Side x equals 1 m

Side x equals 2 m
Side x equals 2 m

Side x equals 13 m
Side x equals 13 m
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Answer 1

To determine the length of the third side of a triangle using the Triangle Inequality Theorem, we need to understand the theorem itself. The Triangle Inequality Theorem states that for any triangle with sides of lengths \(a\), \(b\), and \(c\):

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

You need to know the lengths of the two given sides to find the range for the third side.

Assuming you have two sides of the triangle (let's call them \(a\) and \(b\)), say \(a\) and \(b\), you can calculate the possible length \(x\) (the third side) with the following inequalities:

1. \(x < a + b\)
2. \(x > |a - b|\)

By using the values provided (like 1 m, 2 m, and 13 m), you can check which one of those lengths satisfies the inequalities based on the known sides.

Without the specific lengths of the known sides, it’s impossible to determine the value of \(x\) correctly. However, if you could provide these known side lengths, I would be able to help you further!

Given your responses:
- Side \(x = 1 \, \text{m}\)
- Side \(x = 2 \, \text{m}\)
- Side \(x = 13 \, \text{m}\)

Use the inequalities mentioned to check each option against the known sides. If additional information is provided, we can solve it accurately.