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Let's go over the first question from your homework:

1. **Problem:**  
   Quadrilateral A has side lengths 12, 16, 16, and 24. Quadrilateral B is a scaled copy of Quadrilateral A, with its shortest side of length 3. What is the perimeter of Quadrilateral B?

### Solution:
   - The shortest side of Quadrilateral A is **12**.
   - The shortest side of Quadrilateral B is **3**.
   - To determine the scale factor from Quadrilateral A to B, we divide the shortest side of B by the shortest side of A:

     \[
     \text{Scale factor} = \frac{3}{12} = \frac{1}{4}
     \]

   - Since Quadrilateral B is a scaled copy of Quadrilateral A, each side of Quadrilateral B will be scaled down by this factor.
   - Now, scale each side of Quadrilateral A by \( \frac{1}{4} \):
     - Side 1: \( 12 \times \frac{1}{4} = 3 \)
     - Side 2: \( 16 \times \frac{1}{4} = 4 \)
     - Side 3: \( 16 \times \frac{1}{4} = 4 \)
     - Side 4: \( 24 \times \frac{1}{4} = 6 \)

   - The perimeter of Quadrilateral B is the sum of its side lengths:

     \[
     \text{Perimeter of B} = 3 + 4 + 4 + 6 = 17
     \]

   Therefore, the perimeter of Quadrilateral B is **17 units**.

Would you like assistance with the next problem about the polygon on the grid? Here are five questions to deepen your understanding of similar scaling problems:

1. What happens to the area of a shape when you scale it by a factor of \( \frac{1}{4} \)?
2. If the scale factor between two quadrilaterals was 2, how would you calculate the perimeter of the larger quadrilateral?
3. Can a non-rectangular quadrilateral also be scaled in the same way?
4. How does the perimeter change when the sides of a shape are increased by a scale factor of 3?
5. How would you calculate the perimeter if Quadrilateral A had fractional side lengths?

### Tip:
Always check whether you're scaling the sides by the same factor for all dimensions—this keeps the shape similar in geometry.

Quadrilateral A has side lengths 12, 16, 16, and 24. Quadrilateral B is a scaled copy of Quadrilateral A, with its shortest side of length 3. What is the perimeter of Quadrilateral B?

Learn how to calculate the perimeter of a scaled quadrilateral with side lengths 12, 16, 16, and 24. The problem involves geometry and scaling, making it suitable for Grades 6-8 students. Understand the concept of similar shapes and perimeter calculation with a detailed explanation.

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