The problem involves a triangle with minions posing inside it, and it mentions a scale factor of 3. The task is to fill in the chart and write specific ratios.

Let's break down the image's components and calculations.

PART A: Fill in the chart

Given dimensions:

• The original triangle has sides of 3, 2, and 3.7 units (triangle with minions inside).
• The new image is scaled by a factor of 3.

Using the scale factor, the new dimensions will be:

1. Dimensions of the new image:

   • New side 1: $3 \times 3 = 9$
   • New side 2: $2 \times 3 = 6$
   • New side 3: $3.7 \times 3 = 11.1$

2. Perimeter:

   • Original perimeter = $3 + 2 + 3.7 = 8.7$
   • New perimeter = $9 + 6 + 11.1 = 26.1$

3. Area: The area of a triangle is given by: $\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}$ Assuming the base is 2 and the height is 3, the original area would be: $\text{Original area} = \frac{1}{2} \times 2 \times 3 = 3 \, \text{square units}$ The new area, using the scale factor (area scales by the square of the scale factor): $\text{New area} = 3 \times (3^2) = 3 \times 9 = 27 \, \text{square units}$

PART B: Write the following ratios

• Model length: Actual length = $\frac{1}{3}$
• Model perimeter: Actual perimeter = $\frac{8.7}{26.1} = \frac{1}{3}$
• Model area: Actual area = $\frac{3}{27} = \frac{1}{9}$

Would you like any further details or explanations?

Additional Questions:

1. How would the dimensions change with a scale factor of 4 instead of 3?
2. What if the triangle was not equilateral but had different side lengths?
3. How does the scale factor impact the volume of a 3D shape if the shape was a pyramid?
4. Could you calculate the area using Heron’s formula instead of base-height?
5. What is the relationship between perimeter ratios and area ratios in general?

Tip:

For any shape, area scales by the square of the scale factor, while perimeter scales linearly.