The problem involves using the Pythagoras theorem to find the distance Sam walks. Here's the solution:

Given:

• Alex walks 400 m west.
• Sam walks $x$ meters south.
• The distance between Alex and Sam is 600 m.

Approach:

We are given a right triangle where:

1. The horizontal leg = 400 m (distance Alex walks west).
2. The vertical leg = $x$ m (distance Sam walks south).
3. The hypotenuse = 600 m (distance between Alex and Sam).

By the Pythagoras theorem: $\text{(Hypotenuse)}^2 = \text{(Horizontal leg)}^2 + \text{(Vertical leg)}^2$

Substitute the values: $600^2 = 400^2 + x^2$

Simplify: $360,000 = 160,000 + x^2$

Solve for $x^2$: $x^2 = 360,000 - 160,000$ $x^2 = 200,000$

Take the square root: $x = \sqrt{200,000}$ $x = 447.21 \, \text{m (approximately)}.$

Conclusion:

Sam walks approximately 447.21 meters south.

Would you like further clarification or detailed steps? Let me know!

Related Questions:

1. What is the general formula for applying the Pythagoras theorem?
2. If Alex and Sam were 800 m apart, how far would Sam have to walk?
3. What is the significance of the hypotenuse in a right triangle?
4. How can this problem be solved graphically instead of algebraically?
5. How do we determine whether a triangle is right-angled using the Pythagoras theorem?

Tip:

Always double-check your calculations by substituting your answer back into the original equation. This ensures accuracy!