The problem shows two similar shapes, $S$ and $T$. Shape $S$ has a perimeter of 12 cm, and you are asked to calculate the perimeter of shape $T$.

Since the shapes are similar, their corresponding sides are proportional. From the image, the height of shape $S$ is 4 cm, and the height of shape $T$ is 40 cm.

Step 1: Find the scale factor.

The scale factor is the ratio of corresponding sides of the shapes. The height of shape $T$ is 40 cm, and the height of shape $S$ is 4 cm, so the scale factor $k$ is:

$k = \frac{\text{Height of } T}{\text{Height of } S} = \frac{40}{4} = 10$

Step 2: Use the scale factor to find the perimeter of shape $T$.

Since the perimeter of similar shapes scales by the same factor as their corresponding sides, the perimeter of shape $T$ is:

$\text{Perimeter of } T = k \times \text{Perimeter of } S = 10 \times 12 = 120 \, \text{cm}$

Thus, the perimeter of shape $T$ is 120 cm.

Would you like further details or have any questions? Here are 5 related questions to explore:

1. What is the relationship between the areas of similar shapes?
2. How do you calculate the area of a shape when given the perimeter and other side lengths?
3. Can the same method be applied to three-dimensional shapes?
4. How would the problem change if the scale factor were fractional?
5. What is the effect of increasing the scale factor on the perimeter and area?

Tip: When dealing with similar shapes, remember that lengths, perimeters, and areas scale differently: lengths and perimeters scale linearly, while areas scale with the square of the scale factor.