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

To solve this problem, we can use the Pythagorean theorem because the path John takes forms a right triangle. The 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.

Here are the steps:

1. Identify the lengths of the two sides of the right triangle. In this case, one side is the distance John walks south (12 km) and the other side is the distance he walks west (16 km).

2. Square each of these distances: 12^2 = 144 and 16^2 = 256.

3. Add these two squares together: 144 + 256 = 400.

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

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