4. Quadrilateral A has side lengths 3, 6, 6, and 9. Quadrilateral Bis a scaled copy of A with a shortest side length equal to 2. jada says, "Since the side lengths go down by 1 in this scaling, the perimeter goes down by 4 in total." Do you agree with Jada? Explain your reasoning.

I do not agree with Jada's reasoning. 

Jada seems to be assuming that since the shortest side length of Quadrilateral B is 1 unit less than that of Quadrilateral A (from 3 to 2), the other side lengths will also decrease by 1. However, this is not how scaling works in geometry. Scaling a shape means multiplying all side lengths by the same factor, not subtracting a fixed number from each side.

Let’s break it down:

1. **Side lengths of Quadrilateral A**: 3, 6, 6, and 9.
2. **Shortest side of Quadrilateral B**: 2.

To find the scaling factor, we compare the shortest sides of both quadrilaterals:
\[
\text{Scaling factor} = \frac{\text{Shortest side of B}}{\text{Shortest side of A}} = \frac{2}{3}.
\]

Since Quadrilateral B is a scaled copy of A, all of its side lengths must be scaled by this factor. Therefore, the side lengths of Quadrilateral B would be:
- \( 3 \times \frac{2}{3} = 2 \),
- \( 6 \times \frac{2}{3} = 4 \),
- \( 6 \times \frac{2}{3} = 4 \),
- \( 9 \times \frac{2}{3} = 6 \).

Thus, the side lengths of Quadrilateral B are 2, 4, 4, and 6.

### Calculating Perimeters:
- **Perimeter of A** = \( 3 + 6 + 6 + 9 = 24 \).
- **Perimeter of B** = \( 2 + 4 + 4 + 6 = 16 \).

### Conclusion:
The perimeter of B is 16, which is 8 units less than the perimeter of A (not 4). This difference occurs because the side lengths are scaled by a factor of \( \frac{2}{3} \), not decreased by 1.

Jada's reasoning is incorrect because she didn't consider the scaling factor properly. The perimeter decreases by a proportion related to the scaling factor, not by a fixed amount.

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Would you like more details on scaling factors or how to calculate scaled side lengths?

Here are five related questions for further exploration:

1. How do you determine the scaling factor for any two similar shapes?
2. What happens to the perimeter of a shape when it is scaled by a factor greater than 1?
3. How is the area of a shape affected by scaling its side lengths?
4. Can scaling ever change the angles of a shape?
5. How do scaling transformations relate to real-world applications like model-building?

**Tip**: When scaling a figure, remember that both the perimeter and the area change, but not in the same way. The perimeter scales linearly, while the area scales by the square of the scaling factor.

Quadrilateral A has side lengths 3, 6, 6, and 9. Quadrilateral B is a scaled copy of A with a shortest side length equal to 2. Jada says, 'Since the side lengths go down by 1 in this scaling, the perimeter goes down by 4 in total.' Do you agree with Jada? Explain your reasoning.

Understand how scaling affects the side lengths and perimeter of quadrilaterals. In this problem, Quadrilateral B is a scaled copy of Quadrilateral A, with side lengths and perimeters analyzed using a scaling factor. Suitable for students in Grades 6-8.

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