Geometry

Question Analysis

This question is centered around applying the Pythagorean inequality theorems to classify a triangle. The main task is to figure out if the triangle is acute, right, or obtuse by comparing the squares of its side lengths.

 

Key Concept Explanation

Pythagorean Theorem: For a right triangle with legs and 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 10, 15, and 18, the longest side . Let and .

2. Calculate and :

Calculate :

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