Ian leaves and walks 12 km due south from work, turns and walks 16 km west to get to school.How far would Ian 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 Ian 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 paths Ian walks: 12 km south and 16 km west. So, a = 12 km and b = 16 km.

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

3. Add these two squares together: a² + b² = 144 km² + 256 km² = 400 km².

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

So, Ian would need to walk 20 km in a straight line to get back to work.