A man travels 3 km north, then 4 km east. What is the shortest distance back to

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Question: A man travels 3 km north, then 4 km east. What is the shortest distance back to his starting point?

Options:

Correct Answer: 5 km

Solution:

Using the Pythagorean theorem, the shortest distance is 5 km.

A man travels 3 km north, then 4 km east. What is the shortest distance back to his starting point?

A man travels 3 km north, then 4 km east. What is the shortest distance back to his starting point?

Step 1: Understand that the man travels 3 km north and then 4 km east.
Step 2: Visualize the man's path as a right triangle, where one side is 3 km (north) and the other side is 4 km (east).
Step 3: Identify that the shortest distance back to the starting point is the hypotenuse of this right triangle.
Step 4: Use the Pythagorean theorem, which states that a² + b² = c², where 'c' is the hypotenuse.
Step 5: Calculate a² (3 km)² = 9 and b² (4 km)² = 16.
Step 6: Add these values: 9 + 16 = 25.
Step 7: Find the square root of 25 to get the hypotenuse: √25 = 5 km.
Step 8: Conclude that the shortest distance back to the starting point is 5 km.

Pythagorean Theorem – A mathematical principle used to calculate the length of the sides of a right triangle, stating that the square of the hypotenuse is equal to the sum of the squares of the other two sides.