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?
Answers
GPT-4o mini
To find the area of the dilated rectangle, we start with the original dimensions of the rectangle, which are 4 inches and 10 inches.
First, we calculate the area of the original rectangle:
\[
\text{Area} = \text{length} \times \text{width} = 4 \, \text{inches} \times 10 \, \text{inches} = 40 \, \text{square inches}
\]
Next, we apply the dilation using a scale factor of 2.5. The new dimensions after dilation are:
\[
\text{New length} = 2.5 \times 10 \, \text{inches} = 25 \, \text{inches}
\]
\[
\text{New width} = 2.5 \times 4 \, \text{inches} = 10 \, \text{inches}
\]
Now, we can calculate the area of the dilated rectangle:
\[
\text{Area of dilated rectangle} = \text{New length} \times \text{New width} = 25 \, \text{inches} \times 10 \, \text{inches} = 250 \, \text{square inches}
\]
Therefore, the area of the dilated rectangle is
\[
\boxed{250} \, \text{square inches}.
\]
First, we calculate the area of the original rectangle:
\[
\text{Area} = \text{length} \times \text{width} = 4 \, \text{inches} \times 10 \, \text{inches} = 40 \, \text{square inches}
\]
Next, we apply the dilation using a scale factor of 2.5. The new dimensions after dilation are:
\[
\text{New length} = 2.5 \times 10 \, \text{inches} = 25 \, \text{inches}
\]
\[
\text{New width} = 2.5 \times 4 \, \text{inches} = 10 \, \text{inches}
\]
Now, we can calculate the area of the dilated rectangle:
\[
\text{Area of dilated rectangle} = \text{New length} \times \text{New width} = 25 \, \text{inches} \times 10 \, \text{inches} = 250 \, \text{square inches}
\]
Therefore, the area of the dilated rectangle is
\[
\boxed{250} \, \text{square inches}.
\]