Geometry

Question Analysis

The main focus is to use the Pythagorean Theorem Converse to check if the given side lengths can form a right - triangle. We need to find out if the sum of the squares of the two shorter sides equals the square of the longest side.

 

Key Concept Explanation

The Pythagorean Theorem Converse states that for a triangle with side lengths , , and  (where  is the longest side), if , then the triangle is a right - triangle.

 

Step - by - Step Solution

1. Identify the longest side:

 Calculate the squares of the given sides: , , and .

 Comparing 37, 53 and 144, the longest side , and the two shorter sides are  and

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