Geometry

Question Analysis

The main focus is to apply the Pythagorean Theorem Converse to check if the given triangle is a right - triangle. We must compare 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 longest side:

 Calculate the squares of the sides: , , .

 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:

 

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