Geometry

Question Analysis

This question is about using Pythagorean inequality theorems. The main task is to figure out the triangle type 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 with side lengths , , and (where is the longest side), if , the triangle is a right triangle; if > , it's an acute triangle; if < , it's an obtuse triangle.

Step-by-Step Solution

Let , , and (since 12 is the longest side). Calculate : . Calculate

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