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.