Geometry

Question Analysis

The main focus is to use the Triangle Inequality Theorem to determine which set of side lengths can form a triangle. This requires checking if the sum of any two sides in each set is greater than the third side.

Key Concept Explanation

The Triangle Inequality Theorem states that for any triangle with side lengths , , and , the following three inequalities must hold: a + b>c, a + c>b, and b + c>a. Geometrically, this ensures that the sides can be arranged to enclose an area.

Step - by - Step Solution

1. For the set :

Check 7+8 = 15>14.

Check 7 + 14=21>8.

Check 8 + 14 = 22>7. All inequalities hold.

2. For the set :

Calculate

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