To determine the area of the dilated rectangle, we first need to find the new dimensions after dilation.
The dimensions of the original rectangle are:
- Length = 10 inches
- Width = 4 inches
When dilating a rectangle, each dimension is multiplied by the scale factor. Here, the scale factor is 2.5.
New Length = \( 10 , \text{inches} \times 2.5 = 25 , \text{inches} \)
New Width = \( 4 , \text{inches} \times 2.5 = 10 , \text{inches} \)
Next, we calculate the area of the dilated rectangle using the formula for the area of a rectangle, which is: \[ \text{Area} = \text{Length} \times \text{Width} \]
Substituting the new dimensions into the formula: \[ \text{Area} = 25 , \text{inches} \times 10 , \text{inches} = 250 , \text{square inches} \]
Thus, the area of the dilated rectangle is \( \boxed{250} \).