Geometry

Question Analysis

The main focus is to identify the correct application of the Pythagorean Theorem to find the equation for the unknown side  in the right - triangle. We need to correctly match the sides of the triangle with the terms in the Pythagorean formula.

 

Key Concept Explanation

The Pythagorean Theorem states that for a right - triangle with legs of lengths  and  and hypotenuse of length , . The hypotenuse is the side opposite the right angle and is the longest side of the right - triangle.

 

Step - by - Step Solution

1. Identify the sides of the right - triangle:

In the given triangle, the two legs have lengths 9 and 13, and the side we want to find, , is the hypotenuse.

2. Apply the Pythagorean Theorem:

Substitute the values of the legs (, ) and the hypotenuse () into the formula

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