John leaves and walks 9 km due north from work, turns and walks 12 km east to get home.How far would John need to walk in a straight line to get back to work?

To solve this problem, we can use the Pythagorean theorem because the path John 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'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 John walks north and east, which are 9 km and 12 km respectively.

2. Substitute these values into the Pythagorean theorem: (9 km)² + (12 km)² = c².

3. Calculate the squares: 81 km² + 144 km² = c².

4. Add the squares together: 225 km² = c².

5. Take the square root of both sides to solve for c (the hypotenuse). The square root of 225 km² is 15 km.

So, John would need to walk 15 km in a straight line to get back to work.