Geometry

Question Analysis

The main focus is to use the Pythagorean Theorem to find the length of the diagonal path (the hypotenuse of the right - triangle formed by Tom's east - and north - bound paths), and then calculate the total distance he walked by summing the lengths of all three paths.

Key Concept Explanation

The Pythagorean Theorem states that for a right - triangle with legs of lengths  and  and hypotenuse of length , . This is used to find the unknown side length in a right - triangle, which is crucial for solving this problem.

Step - by - Step Solution

1. Find the length of the diagonal path:

The two legs of the right - triangle are  feet and  feet.

By the Pythagorean Theorem .

Substitute the values: .

Calculate  and

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