Geometry

Question Analysis

The main focus is to utilize the Pythagorean Theorem Converse to determine if the given triangle is a right - triangle by comparing the sum of the squares of the two shorter sides with the square of the longest side.

 

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.

 

Step - by - Step Solution

1. Identify the sides:

 First, find the squares of the sides: , , .

 By comparing the values, the longest side , and the two shorter sides are  and .

2. Calculate the sum of the squares of the two shorter sides:

 Calculate , where  and

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