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:

The two shorter sides are  inches and  inches.

The longest side is  inches.

2. Calculate the squares:

.

.

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