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.