Benjamin leaves and walks 12 km due north from the store, turns and walks 16 km west to get to school.How far would Benjamin need to walk in a straight line to get back to the store?

To solve this problem, we can use the Pythagorean theorem, which 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, Benjamin's path forms a right triangle. The distance he walks north can be one side of the triangle (a = 12 km), the distance he walks west can be the second side (b = 16 km), and the straight-line distance from the school back to the store is the hypotenuse (c).

1. First, square the lengths of the two sides: a² = 12² = 144 km² and b² = 16² = 256 km².
2. Then, add these two values together: a² + b² = 144 km² + 256 km² = 400 km².
3. Finally, take the square root of this sum to find the length of the hypotenuse: c = √400 = 20 km.

So, Benjamin would need to walk 20 km in a straight line to get back to the store.