Question

a rectangle measures 5 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?

312.5
250
50
100
278.3

Answer 1

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

The original dimensions of the rectangle are:
- Width = 5 inches
- Length = 10 inches

The scale factor for dilation is 2.5. To find the new dimensions, we multiply each dimension by the scale factor:

1. New Width = \(5 \text{ inches} \times 2.5 = 12.5 \text{ inches}\)
2. New Length = \(10 \text{ inches} \times 2.5 = 25 \text{ inches}\)

Now, we can calculate the area of the dilated rectangle using the formula for the area of a rectangle, which is:

\[
\text{Area} = \text{Width} \times \text{Length}
\]

Substituting in our new dimensions:

\[
\text{Area} = 12.5 \text{ inches} \times 25 \text{ inches} = 312.5 \text{ square inches}
\]

Thus, the area of the dilated rectangle is **312.5 square inches**.