Geometry

Question Analysis

This question involves the application of the Pythagorean Theorem Converse. The main focus is to determine which set of side lengths does not satisfy the condition for a right triangle, that is, the sum of the squares of the two shorter sides is not equal to the square of the longest side according to the Pythagorean Theorem Converse.

 

Key Concept Explanation

The Pythagorean Theorem Converse states that for a triangle with side lengths , , and (where is the longest side), if , then the triangle is a right triangle. If , the triangle is not a right triangle.

 

Step - by - Step Solution

A. For the set :

Calculate : .

Calculate : .

Since , this set of side lengths creates a right triangle.

 

B. For the set :

Calculate : .

Calculate : .

Since , this set of side lengths does not create a right triangle.

 

C. For the set

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