To find the area of the dilated rectangle, we first need to determine the dimensions of the rectangle after dilation.
The original rectangle measures 4 inches by 10 inches. When dilated using a scale factor of 2.5:
- The new length: \( 10 , \text{inches} \times 2.5 = 25 , \text{inches} \)
- The new width: \( 4 , \text{inches} \times 2.5 = 10 , \text{inches} \)
Now, we can calculate the area of the dilated rectangle:
\[ \text{Area} = \text{length} \times \text{width} \] \[ \text{Area} = 25 , \text{inches} \times 10 , \text{inches} = 250 , \text{square inches} \]
Thus, the area of the dilated rectangle is \( \boxed{250} \) square inches.
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