A person travels 5 km north, then 5 km west. What is the shortest distance back

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Question: A person travels 5 km north, then 5 km west. What is the shortest distance back to the starting point?

Options:

Correct Answer: 7 km

Solution:

The shortest distance back is √(5² + 5²) = 7 km.

A person travels 5 km north, then 5 km west. What is the shortest distance back to the starting point?

A person travels 5 km north, then 5 km west. What is the shortest distance back to the starting point?

Step 1: Understand that the person travels 5 km north and then 5 km west.
Step 2: Visualize the path as a right triangle where one leg is 5 km (north) and the other leg is 5 km (west).
Step 3: Use the Pythagorean theorem to find the shortest distance back to the starting point. The theorem states that the square of the hypotenuse (the shortest distance) is equal to the sum of the squares of the other two sides.
Step 4: Calculate the squares of the two sides: 5² = 25 and 5² = 25.
Step 5: Add the two squares together: 25 + 25 = 50.
Step 6: Take the square root of the sum to find the hypotenuse: √50.
Step 7: Simplify √50 to get √(25 * 2) = 5√2, which is approximately 7.07 km.

Pythagorean Theorem – The problem involves calculating the shortest distance between two points using the Pythagorean theorem, which applies to right triangles.