The image shows a right-angled triangle $\triangle HFG$, where:

• $FH = 6 \, \text{cm}$
• $HG = 15 \, \text{cm}$
• $FG$ is the hypotenuse, which we are asked to find using Pythagoras' theorem.

Applying Pythagoras' Theorem:

Pythagoras' theorem states that, in a right-angled triangle: $FG^2 = FH^2 + HG^2$

Substituting the given values: $FG^2 = 6^2 + 15^2$ $FG^2 = 36 + 225$ $FG^2 = 261$ $FG = \sqrt{261}$ $FG \approx 16.2 \, \text{cm} \quad (\text{to 1 decimal place})$

Thus, the length of $FG$ is approximately 16.2 cm.

Would you like further details or have any questions about this solution?

Related questions:

1. How does Pythagoras' theorem work for non-right-angled triangles?
2. Can Pythagoras' theorem be applied in 3D shapes like cubes?
3. What are some common mistakes when applying Pythagoras' theorem?
4. How can trigonometric ratios help find the angles in this triangle?
5. What are some real-life applications of Pythagoras' theorem?

Tip: Always make sure that the triangle is a right-angled one before applying Pythagoras' theorem.