John leaves and walks 6 km due south from the store, turns and walks 8 km west to get home.How far would John need to walk in a straight line to get back to the store?

To solve this problem, we can use the Pythagorean theorem because the path John took 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 John walked: 6 km south and 8 km west. So, a = 6 km and b = 8 km.

2. Square these two distances: a² = (6 km)² = 36 km² and b² = (8 km)² = 64 km².

3. Add these two squares together: a² + b² = 36 km² + 64 km² = 100 km².

4. Take the square root of this sum to find c, the length of the hypotenuse. The square root of 100 km² is 10 km.

So, John would need to walk 10 km in a straight line to get back to the store.