Geometry

Question Analysis

The main focus is to use the Pythagorean Theorem Converse to determine if the given side lengths form a right - triangle. We must check if the sum of the squares of the two shorter sides equals 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, compare the values of the sides to find the longest side.

We know that , , and . So, the longest side , and the two shorter sides are  and .

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

Calculate , where