Answer :
To solve this problem, you need to understand how the area of a geometric figure changes when it is dilated by a scale factor.
Here are the steps to find the new area:
1. Understand the original problem:
- The original area of the rectangle is 15 square inches.
- The rectangle is dilated by a scale factor of 2.
2. Understand dilation:
- Dilation changes the size of a figure by a certain scale factor.
- When dilating a two-dimensional figure, the area changes by the square of the scale factor.
3. Calculate the new scale factor for the area:
- Since the scale factor is 2 for the sides, the scale factor for the area will be [tex]\(2^2\)[/tex].
4. Compute the new area:
- The new area is given by the formula:
[tex]\[ \text{new area} = \text{original area} \times (\text{scale factor})^2 \][/tex]
- Substitute the given values into the formula:
[tex]\[ \text{new area} = 15 \,\text{square inches} \times (2)^2 \][/tex]
5. Perform the calculation:
- [tex]\((2)^2 = 4\)[/tex]
- [tex]\(\text{new area} = 15 \times 4 = 60\, \text{square inches}\)[/tex]
So, the area of the rectangle after it is dilated by a scale factor of 2 will be [tex]\(60\, \text{square inches}\)[/tex].
Here are the steps to find the new area:
1. Understand the original problem:
- The original area of the rectangle is 15 square inches.
- The rectangle is dilated by a scale factor of 2.
2. Understand dilation:
- Dilation changes the size of a figure by a certain scale factor.
- When dilating a two-dimensional figure, the area changes by the square of the scale factor.
3. Calculate the new scale factor for the area:
- Since the scale factor is 2 for the sides, the scale factor for the area will be [tex]\(2^2\)[/tex].
4. Compute the new area:
- The new area is given by the formula:
[tex]\[ \text{new area} = \text{original area} \times (\text{scale factor})^2 \][/tex]
- Substitute the given values into the formula:
[tex]\[ \text{new area} = 15 \,\text{square inches} \times (2)^2 \][/tex]
5. Perform the calculation:
- [tex]\((2)^2 = 4\)[/tex]
- [tex]\(\text{new area} = 15 \times 4 = 60\, \text{square inches}\)[/tex]
So, the area of the rectangle after it is dilated by a scale factor of 2 will be [tex]\(60\, \text{square inches}\)[/tex].
