Geometry

Question Analysis

This question focuses on classifying a triangle based on its side lengths using the Pythagorean inequality theorems. The key is to determine the relationship between the squares of the side lengths to decide if the triangle is acute, right, or obtuse.

 

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 sides: Let , , and (where is the longest side).

2. Calculate

Click "Show Answer" to reveal the answer and analysis