To find the area of the dilated rectangle, we first need to determine the dimensions of the original rectangle and then apply the scale factor.
The original rectangle measures:
- Length = 10 inches
- Width = 4 inches
The area of the original rectangle is calculated as: \[ \text{Area} = \text{Length} \times \text{Width} = 10 , \text{inches} \times 4 , \text{inches} = 40 , \text{square inches} \]
Next, we dilate the rectangle using a scale factor of 2.5. The new dimensions will be:
- New Length = \(10 , \text{inches} \times 2.5 = 25 , \text{inches}\)
- New Width = \(4 , \text{inches} \times 2.5 = 10 , \text{inches}\)
Now, we can calculate the area of the dilated rectangle: \[ \text{Area of dilated rectangle} = \text{New Length} \times \text{New Width} = 25 , \text{inches} \times 10 , \text{inches} = 250 , \text{square inches} \]
Thus, the area of the dilated rectangle is \(250\) square inches.
The correct response is: 250.
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