Geometry

Question Analysis

This question aims to classify a triangle as acute, right, or obtuse using the Pythagorean inequality theorems. The main 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 - angled 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 longest side:

Given side lengths , , and , the longest side . Let and .

2. Calculate and :

Calculate :

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