Geometry

Question Analysis

The main focus is to use the Pythagorean Theorem Converse to determine if the given side lengths can form a right - triangle. We need to 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 longest side:

Given side lengths are 5 inches, 7 inches, and 9 inches. The longest side inches, and the two shorter sides are inches and inches.

2. Calculate the squares of the sides:

, , and .

3. Check the relationship:

Calculate :

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