Geometry

Question Analysis

This question is about using the Pythagorean inequality theorems to determine if a triangle is acute, right, or obtuse. The main focus is on comparing the sum of the squares of the two shorter sides with the square of the longest side.

 

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. Among , , and , the longest side , and let and .

2. Then calculate and :

Calculate : .

Calculate

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