Christine leaves and walks 6 km due south from work, turns and walks 8 km west to get to school.How far would Christine need to walk in a straight line to get back to work?

Christine's journey forms a right-angled triangle, with her walk from work to school being the hypotenuse. We can use the Pythagorean theorem to find the length of the hypotenuse. The theorem states that in a right-angled 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

where:

• a and b are the lengths of the other two sides
• c is the length of the hypotenuse

In this case, a = 6 km (the distance Christine walked south) and b = 8 km (the distance she walked west). Substituting these values into the equation gives:

6² + 8² = c² 36 + 64 = c² 100 = c²

Taking the square root of both sides gives c = 10. Therefore, Christine would need to walk 10 km in a straight line to get back to work.