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The measures of three line segments are given in each set. Which set of line segments cannot form a triangle?

A. 6 m, 49.9 m, 83.2 m
B. 12.8 m, 25.7 m, 35.9 m
C. 20.2 m, 20.4 m, 20.6 m
D. 32.8 m, 48.2 m, 81.1 m

Answer :

Among the given sets of line segments, the set that cannot form a triangle is 32.8 m, 48.2 m, 81.1 m. The sum of the lengths of the two shorter sides of a triangle must be greater than the length of the longest side. In this particular set, that condition is not satisfied.

To determine if a set of line segments can form a triangle, we apply the triangle inequality theorem. According to this theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. In the set 32.8 m, 48.2 m, 81.1 m, let's check the lengths of the sides. The sum of the two shorter sides is 32.8 m + 48.2 m = 81 m, which is equal to the length of the longest side, 81.1 m. In this case, the sum of the two shorter sides is not greater than the longest side, violating the triangle inequality theorem. Therefore, this set of line segments cannot form a triangle.

To learn more about triangle inequality theorem, click here:

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