Myanmar says  that the area of the large rectangle is 4 times the area of the small rectangle. Convince nynna that this is incorrect. Sketch on the rectangle to support your argument 

To convince Nynna that Myanmar's claim (that the area of the large rectangle is 4 times the area of the small rectangle) is incorrect, we need to analyze the relationship between the two rectangles.

### General Approach:
- **Step 1: Define Dimensions** – Let the dimensions of the small rectangle be:
  - Length = \( l_s \)
  - Width = \( w_s \)
  Then the area of the small rectangle, \( A_s \), is:
  \[
  A_s = l_s \times w_s
  \]

  Similarly, let the dimensions of the large rectangle be:
  - Length = \( l_l \)
  - Width = \( w_l \)
  Then the area of the large rectangle, \( A_l \), is:
  \[
  A_l = l_l \times w_l
  \]

- **Step 2: Analyze Myanmar's Statement** – Myanmar claims that:
  \[
  A_l = 4 \times A_s
  \]
  Which implies:
  \[
  l_l \times w_l = 4 \times (l_s \times w_s)
  \]

- **Step 3: Possible Mistake** – Let's examine possible errors:
  1. **Similar Shapes**: If the rectangles are similar in shape (i.e., the large rectangle has dimensions that are scaled versions of the small one, like \( l_l = 2l_s \) and \( w_l = 2w_s \)), then the area of the large rectangle would be 4 times the area of the small rectangle because:
     \[
     A_l = (2l_s) \times (2w_s) = 4 \times (l_s \times w_s)
     \]
     In this case, Myanmar's claim is **true**.
  2. **Different Aspect Ratios**: If the dimensions of the large rectangle are not simple multiples of the small rectangle, then the area ratio will not be exactly 4. This is where the claim could be incorrect.

### Visual Argument:
I could illustrate this with a sketch, showing both cases:
- A **scaled version** of the small rectangle (which supports Myanmar's claim).
- A **non-scaled version**, where the large rectangle is not simply 2 times longer or wider, but has different proportions, proving that the area ratio might not be exactly 4.

Would you like me to sketch this scenario to clarify the concept visually?

---

**5 Relative Questions**:
1. What happens to the area if the length and width of the large rectangle are not proportional to the small one?
2. How does changing the dimensions of a rectangle impact its area?
3. If the large rectangle’s length was 3 times and width was 2 times the small rectangle’s, what would the area ratio be?
4. Can the ratio of areas be predicted just by looking at the ratios of lengths and widths?
5. How would this analysis change if the rectangles were placed inside one another?

**Tip**: Always check if shapes are proportional when comparing areas based on scaling!

Myanmar says that the area of the large rectangle is 4 times the area of the small rectangle. Convince nynna that this is incorrect. Sketch on the rectangle to support your argument.

Explore how to analyze the area relationship between a large and small rectangle, disproving the claim that one rectangle is 4 times larger than the other. This example explains proportional scaling and how area depends on the product of dimensions, suitable for Grades 6-8.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation