Geometry

Question Analysis

The main focus is to use the Pythagorean Theorem to find the length of the diagonal path (the hypotenuse of a right - triangle formed by Sarah's first two paths), and then calculate the total distance she walked by adding 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 , the equation is . This theorem helps in finding the length of an unknown side in a right - triangle, which is essential for solving this problem.

Step - by - Step Solution

1. Find the length of the diagonal path:

The lengths of the two legs of the right - triangle formed by Sarah's first two paths are  feet and  feet.

According to the Pythagorean Theorem .

Substitute the values: .

Calculate  and