To calculate the perimeter of the right-angled triangle, we need to:

1. Use Pythagoras' theorem to find the hypotenuse ($c$): $c = \sqrt{a^2 + b^2}$ where $a = 3.5 \, \text{cm}$ and $b = 6 \, \text{cm}$.

2. Add the three sides together to find the perimeter: $\text{Perimeter} = a + b + c$

Step 1: Calculate the hypotenuse

$c = \sqrt{3.5^2 + 6^2}$ $c = \sqrt{12.25 + 36}$ $c = \sqrt{48.25}$ $c \approx 6.9 \, \text{cm} \, (\text{to 1 d.p.})$

Step 2: Calculate the perimeter

$\text{Perimeter} = 3.5 + 6 + 6.9$ $\text{Perimeter} = 16.4 \, \text{cm} \, (\text{to 1 d.p.})$

Final Answer:

The perimeter of the triangle is 16.4 cm.

Let me know if you need further explanation or have any questions. Here are some follow-up queries:

1. How is Pythagoras' theorem derived and when is it applicable?
2. What are the properties of a right-angled triangle?
3. How do we calculate the area of the same triangle?
4. What are some real-life applications of Pythagoras' theorem?
5. Can Pythagoras' theorem be extended to non-right triangles? If so, how?

Tip: When solving problems involving square roots, ensure to round off values only in the final step for accuracy.