Question
A rectangle measures 4 inches by 10 inches. It is dilated using a scale factor of 2.5. What is the area in square inches of the dilated rectangle?(1 point) Responses 40 in2 40 in2 160 in2 160 in2 250 in2 250 in2 2,500 in2
Answers
GPT-4o mini
To find the area of the dilated rectangle, we first calculate the area of the original rectangle and then apply the scale factor to determine the dimensions of the dilated rectangle.
1. **Calculate the area of the original rectangle:**
\[
\text{Area} = \text{length} \times \text{width} = 4 \, \text{inches} \times 10 \, \text{inches} = 40 \, \text{square inches}
\]
2. **Dilate the rectangle using a scale factor of 2.5:**
- New length = \(4 \, \text{inches} \times 2.5 = 10 \, \text{inches}\)
- New width = \(10 \, \text{inches} \times 2.5 = 25 \, \text{inches}\)
3. **Calculate the area of the dilated rectangle:**
\[
\text{Area} = \text{new length} \times \text{new width} = 10 \, \text{inches} \times 25 \, \text{inches} = 250 \, \text{square inches}
\]
Therefore, the area of the dilated rectangle is **250 square inches**.
1. **Calculate the area of the original rectangle:**
\[
\text{Area} = \text{length} \times \text{width} = 4 \, \text{inches} \times 10 \, \text{inches} = 40 \, \text{square inches}
\]
2. **Dilate the rectangle using a scale factor of 2.5:**
- New length = \(4 \, \text{inches} \times 2.5 = 10 \, \text{inches}\)
- New width = \(10 \, \text{inches} \times 2.5 = 25 \, \text{inches}\)
3. **Calculate the area of the dilated rectangle:**
\[
\text{Area} = \text{new length} \times \text{new width} = 10 \, \text{inches} \times 25 \, \text{inches} = 250 \, \text{square inches}
\]
Therefore, the area of the dilated rectangle is **250 square inches**.