Ian leaves and walks 6 km due north from school, turns and walks 8 km east to get home.How far would Ian need to walk in a straight line to get back to school?

To solve this problem, we can use the Pythagorean theorem because the path Ian takes forms a right triangle. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. This can be written as: a² + b² = c².

Here's the step-by-step solution:

1. Identify the lengths of the two sides of the right triangle. In this case, the two sides are the distances Ian walks north and east, which are 6 km and 8 km respectively.

2. Substitute these values into the Pythagorean theorem: (6 km)² + (8 km)² = c².

3. Calculate the squares: 36 km² + 64 km² = c².

4. Add the results: 100 km² = c².

5. Take the square root of both sides to solve for c (the hypotenuse). The square root of 100 km² is 10 km.

So, Ian would need to walk 10 km in a straight line to get back to school.