To solve this, we will need to calculate the perimeter of rectangle $G$ given that rectangles $F$ and $G$ are similar.

Step 1: Understanding the similarity

For two rectangles to be similar, their corresponding sides must be proportional.

• Rectangle $F$ has dimensions 9 m by 4 m.
• Rectangle $G$ has a width of 8 m (this corresponds to the height of $F$).

Let's use the proportion between the heights to find the length of rectangle $G$.

$\frac{\text{height of G}}{\text{height of F}} = \frac{\text{width of G}}{\text{width of F}}$

$\frac{8}{4} = \frac{\text{width of G}}{9}$

This simplifies to:

$\text{width of G} = 9 \times 2 = 18 \, \text{m}$

Step 2: Calculating the perimeter of rectangle G

The formula for the perimeter of a rectangle is:

$P = 2 \times (\text{width} + \text{height})$

Substituting the values for rectangle $G$:

$P = 2 \times (18 + 8) = 2 \times 26 = 52 \, \text{m}$

Thus, the perimeter of rectangle $G$ is 52 meters.

Would you like more details, or do you have any questions?

Here are some related questions you can explore:

1. How do you find the area of rectangle $G$?
2. How would the dimensions change if the height of rectangle $G$ were doubled?
3. If a third rectangle is similar to rectangles $F$ and $G$, how can you determine its dimensions?
4. What are the properties of similar figures in geometry?
5. How does the ratio of areas relate to the ratio of corresponding sides in similar figures?

Tip: When working with similar figures, always remember that the ratio of corresponding sides is constant!