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 2,500 250 250 160 160 40

Answer 1

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**.