https://r2.erweima.ai/mathbot/image/1723945560262jhcu9rkf.jpg

To solve the problem, we need to determine the perimeter of the figure composed of two rectangles, and then simplify the expression in terms of \( g \).

### Given:
- The dimensions of the left rectangle are \( 6g \) (height) and \( g \) (width).
- The dimensions of the right rectangle are \( 12g \) (height) and \( g \) (width).

### Step 1: Identify the outer edges of the figure.

- **Left vertical edge**: This edge is the height of the left rectangle, which is \( 6g \).
- **Right vertical edge**: This edge is the height of the right rectangle, which is \( 12g \).
- **Top horizontal edge**: This edge is the width of the right rectangle, which is \( g \).
- **Bottom horizontal edge**: This edge is the width of the left rectangle, which is also \( g \).

### Step 2: Consider the combined structure.

The figure's perimeter includes:
- The entire left vertical edge \( 6g \).
- The entire right vertical edge \( 12g \).
- The entire top edge \( g \).
- The entire bottom edge \( g \).
- An additional vertical segment, \( 12g - 6g = 6g \), for the difference in height between the two rectangles.

### Step 3: Calculate the perimeter.

The perimeter \( P \) is the sum of all the outer edges:
\[
P = (6g) + (12g) + (g) + (g) + (6g)
\]

### Step 4: Simplify the expression.

Combine the terms:
\[
P = 6g + 12g + g + g + 6g = 26g
\]

### Final Answer:

The perimeter of the figure is \( \boxed{26g} \).

Would you like any additional details or explanations? Here are some related questions to explore:

1. How do you calculate the area of the combined figure?
2. What happens if the rectangles have different widths?
3. How does changing the value of \( g \) affect the perimeter?
4. Can this problem be generalized for other similar figures?
5. How do you determine the perimeter of a complex figure with more than two rectangles?

**Tip:** Always ensure that all parts of the figure are accounted for when calculating the perimeter, especially when dealing with irregular shapes or composite figures.

Learn how to calculate the perimeter of a composite figure formed by two rectangles with varying dimensions. Follow a step-by-step solution including identifying outer edges, combining dimensions, and simplifying expressions in terms of variable \( g \). Suitable for Grades 7-9.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation