Geometry

Question Analysis

This question focuses on classifying a triangle as acute, right, or obtuse by applying the Pythagorean inequality theorems. The core task is to compare 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 sides , , 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. Identify the sides: Let the two shorter sides , , and the longest side .

2. Calculate

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