Geometry

Question Analysis

The key is to apply the Triangle Inequality Theorem to each set of lengths to determine which one cannot form a triangle. The focus is on checking if the sum of any two sides is greater than the third side for all combinations within each set.

Key Concept Explanation

The Triangle Inequality Theorem states that for a triangle with side lengths , , and , the following three inequalities must hold: a + b>c, a + c>b, and b + c>a. This theorem is fundamental in determining the feasibility of constructing a triangle with given side lengths, as it ensures that the three sides can connect to form a closed geometric figure.

Step - by - Step Solution

1. For the set :

17 + 23 = 40>39

17 + 39 = 56>23

23 + 39 = 62>17

All inequalities are satisfied.

2. For the set

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