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This problem asks what happens to the area of a rectangle when both dimensions (length and width) are doubled.

### Step-by-Step Analysis:

1. **Current Area**: 
   The current dimensions are 10 cm (length) and 9 cm (width).  
   The current area \( A \) is:
   \[
   A = \text{length} \times \text{width} = 10 \, \text{cm} \times 9 \, \text{cm} = 90 \, \text{cm}^2
   \]

2. **Doubling Both Dimensions**:  
   When both the length and width are doubled, the new dimensions will be:
   \[
   \text{New length} = 2 \times 10 = 20 \, \text{cm}
   \]
   \[
   \text{New width} = 2 \times 9 = 18 \, \text{cm}
   \]

3. **New Area**:  
   The new area \( A_{\text{new}} \) is:
   \[
   A_{\text{new}} = 20 \, \text{cm} \times 18 \, \text{cm} = 360 \, \text{cm}^2
   \]

4. **Comparison**:  
   To compare the new area to the old area:
   \[
   \frac{A_{\text{new}}}{A} = \frac{360}{90} = 4
   \]
   So, the new area is 4 times the old area.

### Answer:
The correct statement is: **"The new area will be 4 times the old area."**

Would you like more details on this or have any other questions?

Here are 5 related questions to expand your understanding:
1. What happens to the perimeter when both dimensions are doubled?
2. How would the area change if only one dimension is doubled?
3. What is the effect on the area if both dimensions are tripled?
4. How does the area change if both dimensions are halved?
5. Can you calculate the new diagonal of the rectangle when both dimensions are doubled?

**Tip**: When scaling dimensions of shapes, areas scale by the square of the scale factor.

If both dimensions are doubled, then which of the following statements about its area will be true?

Discover how the area of a rectangle changes when both dimensions are doubled. This example uses a 10 cm by 9 cm rectangle and explores the relationship between scaling and area. Suitable for students in Grades 6-8.

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