A person walks 6 km north, then 8 km east. What is the shortest distance back to

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Question: A person walks 6 km north, then 8 km east. What is the shortest distance back to the starting point?

Options:

Correct Answer: 10 km

Solution:

The shortest distance is √(6² + 8²) = 10 km.

A person walks 6 km north, then 8 km east. What is the shortest distance back to the starting point?

A person walks 6 km north, then 8 km east. What is the shortest distance back to the starting point?

Step 1: Understand that the person walks 6 km north and then 8 km east.
Step 2: Visualize the path as a right triangle where one side is 6 km (north) and the other side is 8 km (east).
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 (shortest distance) is equal to the sum of the squares of the other two sides.
Step 4: Calculate the squares of the two sides: 6² = 36 and 8² = 64.
Step 5: Add the two squares together: 36 + 64 = 100.
Step 6: Take the square root of the sum to find the hypotenuse: √100 = 10 km.
Step 7: Conclude that the shortest distance back to the starting point is 10 km.

Pythagorean Theorem – The relationship between the sides of a right triangle, used to calculate the shortest distance (hypotenuse) when given the two perpendicular sides.