A person walks 5 km east, then 5 km north. What is the shortest distance back to

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

Options:

Correct Answer: 7 km

Solution:

The shortest distance is the hypotenuse of a right triangle, which is 7 km.

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

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

Step 1: Understand that the person walks 5 km east and then 5 km north.
Step 2: Visualize the path as a right triangle where one leg is 5 km (east) and the other leg is 5 km (north).
Step 3: Use the Pythagorean theorem to find the hypotenuse (shortest distance back). The formula is a² + b² = c², where a and b are the legs of the triangle and c is the hypotenuse.
Step 4: Calculate a² + b²: (5 km)² + (5 km)² = 25 km² + 25 km² = 50 km².
Step 5: Find c by taking the square root of 50 km²: c = √50 km = √(25 * 2) km = 5√2 km.
Step 6: Approximate √2 as about 1.414, so 5√2 km is approximately 5 * 1.414 km = 7.07 km.
Step 7: Conclude that the shortest distance back to the starting point is approximately 7 km.

Pythagorean Theorem – The relationship between the sides of a right triangle, where the square of the hypotenuse is equal to the sum of the squares of the other two sides.
Distance Calculation – Understanding how to calculate the shortest distance between two points using geometric principles.