Anna leaves and walks 6 km due south from school, turns and walks 8 km west to get to work.How far would Anna 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 Anna 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, the distance Anna walks south can be one side of the triangle (a = 6 km), and the distance she walks west can be the second side (b = 8 km). We want to find the length of the hypotenuse (c), which represents the straight-line distance from work back to school.

Substituting the given values into the Pythagorean theorem gives us:

6² + 8² = c² 36 + 64 = c² 100 = c²

Taking the square root of both sides to solve for c gives:

c = √100 c = 10 km

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