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

2,500
2,500

40
40

160
160

250

Answer 1

To find the area of the dilated rectangle, we first need to determine the dimensions of the rectangle after dilation.

1. **Original dimensions**: The rectangle measures 4 inches by 10 inches.
2. **Dilation**: The scale factor is 2.5.

We calculate the new dimensions after dilation:

- New length = Original length × Scale factor = \(10 \, \text{inches} \times 2.5 = 25 \, \text{inches}\)
- New width = Original width × Scale factor = \(4 \, \text{inches} \times 2.5 = 10 \, \text{inches}\)

Next, we calculate the area of the dilated rectangle:

\[
\text{Area} = \text{Length} \times \text{Width} = 25 \, \text{inches} \times 10 \, \text{inches} = 250 \, \text{square inches}
\]

Thus, the area of the dilated rectangle is **250 square inches**.