Question

Mike bikes 2 miles north and 2 miles west to get from his house to the library. What is the exact mileage of the shortest distance from Mike's house to the library?

Answer 1

The shortest distance from Mike's house to the library is the hypotenuse of a right-angled triangle with sides of 2 miles each, calculated as the square root of 8, which is approximately 2.83 miles.

Step-by-step explanation:

The shortest distance from Mike's house to the library can be calculated using the Pythagorean theorem. Since Mike bikes 2 miles north and then 2 miles west, we can visualize this as a right-angled triangle, where the north and west paths are the perpendicular sides, and the shortest distance is the hypotenuse.

To calculate the hypotenuse (c), we square both sides (2 miles north, which we can call a, and 2 miles west, which we can call b) and take the square root of their sum:

• a² = 2² = 4
• b² = 2² = 4
• c² = a² + b² = 4 + 4 = 8
• c = √8 ≈ 2.83

Therefore, the exact mileage of the shortest distance from Mike's house to the library is √8, which is approximately 2.83 miles.

Answer 2

The shortest distance from Mike's house to the library is the hypotenuse of a right-angled triangle with sides of 2 miles each, calculated as the square root of 8, which is approximately 2.83 miles.

Step-by-step explanation:

The shortest distance from Mike's house to the library can be calculated using the Pythagorean theorem. Since Mike bikes 2 miles north and then 2 miles west, we can visualize this as a right-angled triangle, where the north and west paths are the perpendicular sides, and the shortest distance is the hypotenuse.

To calculate the hypotenuse (c), we square both sides (2 miles north, which we can call a, and 2 miles west, which we can call b) and take the square root of their sum:

• a² = 2² = 4
• b² = 2² = 4
• c² = a² + b² = 4 + 4 = 8
• c = √8 ≈ 2.83

Therefore, the exact mileage of the shortest distance from Mike's house to the library is √8, which is approximately 2.83 miles.