Christine leaves and walks 9 km due north from school, turns and walks 12 km east to get to the store.How far would Christine need to walk in a straight line to get back to school?

To solve this problem, we can use the Pythagorean theorem because it 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, the distance Christine walked north can be one side of the triangle (a = 9 km), the distance she walked east can be the second side (b = 12 km), and the straight-line distance she needs to walk to get back to school is the hypotenuse (c).

Let's substitute the given values into the Pythagorean theorem:

(9 km)² + (12 km)² = c² 81 km² + 144 km² = c² 225 km² = c²

To find c, we need to take the square root of both sides:

c = √225 km² c = 15 km

So, Christine would need to walk 15 km in a straight line to get back to school.