Aluna leaves and walks 9 km due north from the store, turns and walks 12 km west to get home.How far would Aluna 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 Aluna takes forms a right triangle. The theorem states that in a right-angled 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 Aluna walks north and west, which are 9 km and 12 km respectively.

2. Square these two distances: 9² = 81 and 12² = 144.

3. Add these two squares together: 81 + 144 = 225.

4. Find the square root of this sum to find the length of the hypotenuse. The square root of 225 is 15.

So, Aluna would need to walk 15 km in a straight line to get back to the store.