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

To solve this problem, we can use the Pythagorean theorem because it 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, the distance Mary walks north can be one side of the triangle (a = 12 km), the distance she walks east can be the second side (b = 16 km), and the straight-line distance she would need to walk to get back to work is the hypotenuse (c).

Step 1: Substitute the given values into the Pythagorean theorem:

(12 km)² + (16 km)² = c²

Step 2: Square the values:

144 km² + 256 km² = c²

Step 3: Add the squares:

400 km² = c²

Step 4: Take the square root of both sides to solve for c:

c = √400 km²

c = 20 km

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