Geometry

Question Analysis

The main focus is to apply the Pythagorean Theorem to find the length of the return journey (the hypotenuse of a right - triangle) from the marina back to the harbor. Then, calculate the total distance Lily sailed by adding the lengths of all three legs of her journey.

Key Concept Explanation

The Pythagorean Theorem states that for a right - triangle with legs of lengths and and hypotenuse of length , . Here, the two legs of the right - triangle are the 7 - mile northward sail and the 24 - mile eastward sail, and the hypotenuse is the path from the marina back to the harbor.

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.

Using the Pythagorean Theorem .

Substitute the values: .

Calculate and

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