Geometry

Question Analysis

This question is centered around using the Pythagorean inequality theorems to classify a triangle. The main focus is to determine if the given side lengths satisfy the conditions for an acute, right, or obtuse triangle.

 

Key Concept Explanation

Pythagorean Theorem: For a right triangle with legs and and hypotenuse , .

Pythagorean Inequality Theorems:

If  > (where is the longest side), the triangle is acute.

If  < (where is the longest side), the triangle is obtuse.

 

Step - by - Step Solution

1. First, identify the longest side. Here, , , and .

2. Then, calculate and

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