Geometry

Question Analysis

The main focus is to use the Pythagorean Theorem Converse to verify if the triangle with given side lengths is a right - triangle. We need to check the relationship between the sum of the squares of the two shorter sides and 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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