https://file.aiquickdraw.com/mathbot/file/1726746450870m50blbfd.jpg

This worksheet focuses on scaling a picture using a given scale factor, specifically a scale factor of 10, and understanding how this affects the dimensions, perimeter, and area of the picture.

Here's how we can approach this:

1. **Scale factor**: The original image is being enlarged by a scale factor of 10. This means that all linear dimensions of the new image (length and width) will be 10 times those of the original image.

2. **Dimensions**:
   - The original image has a height of 5 units and a width of 10 units (as per the measurements labeled in the image).
   - To calculate the new dimensions, multiply each dimension by the scale factor:
     - New height = 5 units × 10 = 50 units.
     - New width = 10 units × 10 = 100 units.

3. **Perimeter**:
   - The perimeter of a rectangle is calculated by the formula: 
     \[
     \text{Perimeter} = 2 \times (\text{height} + \text{width})
     \]
   - Original perimeter: 
     \[
     2 \times (5 + 10) = 2 \times 15 = 30 \text{ units}
     \]
   - New perimeter:
     \[
     2 \times (50 + 100) = 2 \times 150 = 300 \text{ units}
     \]

4. **Area**:
   - The area of a rectangle is calculated by:
     \[
     \text{Area} = \text{height} \times \text{width}
     \]
   - Original area:
     \[
     5 \times 10 = 50 \text{ square units}
     \]
   - New area:
     \[
     50 \times 100 = 5000 \text{ square units}
     \]

Now, filling out the chart on the worksheet:
- **Dimensions**:
  - Original image: Height = 5 units, Width = 10 units
  - New image: Height = 50 units, Width = 100 units
- **Perimeter**:
  - Original image: 30 units
  - New image: 300 units
- **Area**:
  - Original image: 50 square units
  - New image: 5000 square units

### Ratios (Part B):
- **Model length : Actual length** = \( \frac{1}{10} \)
- **Model perimeter : Actual perimeter** = \( \frac{30}{300} = \frac{1}{10} \)
- **Model area : Actual area** = \( \frac{50}{5000} = \frac{1}{100} \)

Would you like any further details or have any questions on this?

### Related Questions:
1. What happens to the perimeter when the scale factor is doubled?
2. How is the area affected by doubling the scale factor?
3. Can you derive a formula for how the area changes with respect to the scale factor?
4. Why does the ratio of area change by the square of the scale factor?
5. How would the dimensions change if the scale factor were less than 1?

### Tip:
Remember, for two-dimensional shapes, the area increases by the square of the scale factor, while the perimeter increases linearly by the scale factor.

How does scale factor affect the area and perimeter of figures? Ms. Bisal is making a poster of Captain America Minion with a scale factor of 10. Calculate the new dimensions, perimeter, and area of the image, and write ratios of model length to actual length, perimeter, and area.

Learn how to scale a drawing using a scale factor of 10 and calculate the new dimensions, perimeter, and area. This worksheet problem helps students understand the relationship between scale factor, perimeter, and area with clear calculations.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation