The problem states that the two figures are similar. This means the corresponding sides of the two figures are proportional.

We are given the following information:

• For the smaller figure:

  • One side is 3 cm
  • Another side is 4 cm

• For the larger figure:

  • The side corresponding to the 3 cm side is 5 cm
  • The side corresponding to the 4 cm side is $x$ cm (this is what we need to find)

To solve for $x$, we can set up a proportion based on the similarity of the figures:

$\frac{3}{5} = \frac{4}{x}$

Now, cross-multiply to solve for $x$:

$3x = 5 \times 4$

$3x = 20$

$x = \frac{20}{3} \approx 6.67 \text{ cm}$

So, the value of $x$ is approximately 6.67 cm.

Would you like further details or have any questions? Here are some related questions:

1. How do we define similar figures in geometry?
2. What other types of problems can be solved using proportions?
3. How do we solve proportions when more than two figures are involved?
4. Can you explain how scale factors work in relation to similar figures?
5. How would this problem change if the larger figure had more complex sides?

Tip: Always double-check the corresponding sides when working with similar figures to ensure the proportion is set up correctly.