Geometry

Question Analysis

This question pertains to Pythagorean inequality theorems. The core task is to classify the triangle type using the lengths of its sides, achieved by comparing the sum of the squares of the two shorter sides with the square of the longest side.

 

Key Concept Explanation:

For a triangle having side lengths , , and (where is the longest side):

If , it's a right triangle.

If > , it's an acute triangle.

If < , it's an obtuse triangle.

 

Step-by-Step Solution

Let , , and (as is the longest side).

First, compute :

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