Geometry

Question Analysis

The main focus is to use the Pythagorean Theorem Converse to check if the given triangle is a right - triangle. We need to 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 sides:

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

 By comparing these values, we can see that the longest side , and the two shorter sides are  and .

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

 Calculate , where

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