Question

DeeDee draws a rectangle with sides measuring x inches and y inches. She dilates the rectangle using a scale factor of 14 . What is the area of the original rectangle in terms of x and y? What is the area of the dilated rectangle? How many times greater is the area of the original rectangle compared to the area of the dilated rectangle? Explain your answers and show all your work.(4 points)

Answer 1

To solve the problem, let's break it down step by step.

Step 1: Area of the Original Rectangle

The area \( A \) of a rectangle is calculated using the formula: \[ A = \text{length} \times \text{width} \] For the original rectangle with sides measuring \( x \) inches and \( y \) inches, the area \( A_{\text{original}} \) is: \[ A_{\text{original}} = x \times y \]

Step 2: Area of the Dilated Rectangle

When DeeDee dilates the rectangle using a scale factor of 14, both the length and the width are multiplied by 14. Therefore, the new dimensions of the dilated rectangle are: \[ \text{New length} = 14x \quad \text{and} \quad \text{New width} = 14y \] Now, we can find the area of the dilated rectangle \( A_{\text{dilated}} \): \[ A_{\text{dilated}} = \text{New length} \times \text{New width} = (14x) \times (14y) = 196xy \]

Step 3: Comparing the Areas

Now, we need to find out how many times greater the area of the dilated rectangle is compared to the area of the original rectangle.

The area of the original rectangle is \( A_{\text{original}} = xy \) and the area of the dilated rectangle is \( A_{\text{dilated}} = 196xy \). To find out how many times greater the area of the dilated rectangle is compared to the original rectangle, we can set up the following ratio: \[ \text{Ratio} = \frac{A_{\text{dilated}}}{A_{\text{original}}} = \frac{196xy}{xy} = 196 \]

Conclusion

• The area of the original rectangle is \( xy \).
• The area of the dilated rectangle is \( 196xy \).
• The area of the dilated rectangle is 196 times greater than the area of the original rectangle.

So, to summarize:

• Area of original rectangle: \( xy \)
• Area of dilated rectangle: \( 196xy \)
• The area of the dilated rectangle is 196 times greater than the area of the original rectangle.

Answer 2

make all text copyable

Answer 3

Sure! Here’s the text in a copyable format:

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To solve the problem, let's break it down step by step.

Step 1: Area of the Original Rectangle

The area \( A \) of a rectangle is calculated using the formula:
\[ A = \text{length} \times \text{width} \]
For the original rectangle with sides measuring \( x \) inches and \( y \) inches, the area \( A_{\text{original}} \) is:
\[ A_{\text{original}} = x \times y \]

Step 2: Area of the Dilated Rectangle

When DeeDee dilates the rectangle using a scale factor of 14, both the length and the width are multiplied by 14. Therefore, the new dimensions of the dilated rectangle are:
\[ \text{New length} = 14x \quad \text{and} \quad \text{New width} = 14y \]
Now, we can find the area of the dilated rectangle \( A_{\text{dilated}} \):
\[ A_{\text{dilated}} = \text{New length} \times \text{New width} = (14x) \times (14y) = 196xy \]

Step 3: Comparing the Areas

Now, we need to find out how many times greater the area of the dilated rectangle is compared to the area of the original rectangle.

The area of the original rectangle is \( A_{\text{original}} = xy \) and the area of the dilated rectangle is \( A_{\text{dilated}} = 196xy \). To find out how many times greater the area of the dilated rectangle is compared to the original rectangle, we can set up the following ratio:
\[ \text{Ratio} = \frac{A_{\text{dilated}}}{A_{\text{original}}} = \frac{196xy}{xy} = 196 \]

Conclusion

• The area of the original rectangle is \( xy \).
• The area of the dilated rectangle is \( 196xy \).
• The area of the dilated rectangle is 196 times greater than the area of the original rectangle.

So, to summarize:

• Area of original rectangle: \( xy \)
• Area of dilated rectangle: \( 196xy \)
• The area of the dilated rectangle is 196 times greater than the area of the original rectangle.

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Feel free to copy the above text!

Answer 4

i dont think you changed it much because there are still non copyable parts

so make it all plain text

Answer 5

Certainly! Here is the content in plain text format:

---

To solve the problem, let's break it down step by step.

Step 1: Area of the Original Rectangle

The area A of a rectangle is calculated using the formula: A = length × width For the original rectangle with sides measuring x inches and y inches, the area A_original is: A_original = x × y

Step 2: Area of the Dilated Rectangle

When DeeDee dilates the rectangle using a scale factor of 14, both the length and the width are multiplied by 14. Therefore, the new dimensions of the dilated rectangle are: New length = 14x and New width = 14y Now, we can find the area of the dilated rectangle A_dilated: A_dilated = New length × New width = (14x) × (14y) = 196xy

Step 3: Comparing the Areas

Now, we need to find out how many times greater the area of the dilated rectangle is compared to the area of the original rectangle.

The area of the original rectangle is A_original = xy and the area of the dilated rectangle is A_dilated = 196xy. To find out how many times greater the area of the dilated rectangle is compared to the original rectangle, we can set up the following ratio: Ratio = A_dilated / A_original = (196xy) / (xy) = 196

Conclusion

• The area of the original rectangle is xy.
• The area of the dilated rectangle is 196xy.
• The area of the dilated rectangle is 196 times greater than the area of the original rectangle.

So, to summarize:

• Area of original rectangle: xy
• Area of dilated rectangle: 196xy
• The area of the dilated rectangle is 196 times greater than the area of the original rectangle.

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You can now copy this text easily!

Answer 6

thanks

Answer 7

You're welcome! If you have any more questions or need further assistance, feel free to ask. Happy studying!