Geometry

Question Analysis

The main focus is to use the Pythagorean Theorem to determine the length of the return journey (the hypotenuse of a right - triangle) from the museum back home. After that, calculate the total distance John walked by adding up the lengths of all three parts of his trip.

Key Concept Explanation

The Pythagorean Theorem states that for a right - triangle with legs of lengths and and hypotenuse of length , the equation is . Here, the two legs of the right - triangle are the 5 - mile southward walk and the 12 - mile eastward walk, and the hypotenuse is the path from the museum to home.

Step - by - Step Solution

1. Find the length of the return path:

The lengths of the two legs of the right - triangle are miles and miles.

Applying the Pythagorean Theorem .

Substitute the values: .

Calculate and

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