Anna leaves and walks 12 km due north from home, turns and walks 16 km east to get to work.How far would Anna need to walk in a straight line to get back home?

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 are the steps to find the distance:

1. Identify the lengths of the two sides of the right triangle. In this case, the two sides are the paths that Anna walks: 12 km north and 16 km east. So, a = 12 km and b = 16 km.

2. Square each of these distances: a² = (12 km)² = 144 km² and b² = (16 km)² = 256 km².

3. Add these squared distances together: a² + b² = 144 km² + 256 km² = 400 km².

4. Take the square root of this sum to find c, the length of the hypotenuse. The square root of 400 km² is 20 km.

So, Anna would need to walk 20 km in a straight line to get back home.