Geometry

Question Analysis

This question focuses on using the Pythagorean inequality theorems to classify a triangle. The main task is to determine the type of triangle (acute, right, or obtuse) by comparing the sum of the squares of the two shorter sides with the square of the longest side.

 

Key Concept Explanation

Pythagorean Theorem: In a right - angled triangle, if the lengths of the two legs are and , and the length of the hypotenuse is , then .

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 :