https://file.aiquickdraw.com/mathbot/file/1726715012908dacqwtqv.jpg

To solve the problem in the image, we'll calculate the perimeter and area of both the given rectangle and the dilated rectangle. Let's go step by step:

### 1. Given Rectangle Dimensions:
- Length = 11 units
- Width = 10 units

#### Perimeter of the given rectangle:
The formula for the perimeter \( P \) of a rectangle is:
\[
P = 2 \times (\text{Length} + \text{Width})
\]
Substituting the values:
\[
P = 2 \times (11 + 10) = 2 \times 21 = 42 \text{ units}
\]

#### Area of the given rectangle:
The formula for the area \( A \) of a rectangle is:
\[
A = \text{Length} \times \text{Width}
\]
Substituting the values:
\[
A = 11 \times 10 = 110 \text{ units}^2
\]

### 2. Dilated Rectangle:
The rectangle is dilated by a scale factor of 4. This means that both the length and width will be multiplied by 4.

#### Dimensions of the dilated rectangle:
- New Length = \( 4 \times 11 = 44 \) units
- New Width = \( 4 \times 10 = 40 \) units

#### Perimeter of the dilated rectangle:
Using the perimeter formula:
\[
P_{\text{dilated}} = 2 \times (\text{New Length} + \text{New Width}) = 2 \times (44 + 40) = 2 \times 84 = 168 \text{ units}
\]

#### Area of the dilated rectangle:
Using the area formula:
\[
A_{\text{dilated}} = \text{New Length} \times \text{New Width} = 44 \times 40 = 1760 \text{ units}^2
\]

### Final Answers:
- **Perimeter of the given rectangle**: 42 units
- **Area of the given rectangle**: 110 units²
- **Perimeter of the dilated rectangle**: 168 units
- **Area of the dilated rectangle**: 1760 units²

Do you have any questions or would you like more details on any of the steps?

---

Here are 5 related questions to expand your understanding:
1. What happens to the area of a shape when it is dilated by a scale factor \( k \)?
2. How does the perimeter of a rectangle change when it is dilated?
3. What is the formula for finding the perimeter and area of other quadrilaterals, such as squares?
4. If the scale factor were halved, how would the dimensions of the dilated rectangle change?
5. How does dilation affect three-dimensional shapes?

**Tip:** The area of a dilated shape is scaled by the square of the scale factor, while the perimeter is scaled directly by the scale factor.

The rectangle below is dilated by a scale factor of 4. Find the perimeter and area of the rectangle below, as well as the perimeter and area of the dilated rectangle.

Learn how to find the perimeter and area of a rectangle and its dilated version with a scale factor of 4. Detailed solution including key geometry concepts, formulas for perimeter and area, and how dilation affects dimensions. Suitable for students in Grades 6-8.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation