Question

A rectangle measures 3 inches by 4 inches. It is dilated using a scale factor of 3.

What is the area in square inches of the dilated rectangle?

Answer 1

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

The original rectangle has dimensions:
- Width = 3 inches
- Height = 4 inches

When the rectangle is dilated using a scale factor of 3, we multiply each dimension by the scale factor:

\[
\text{Dilated width} = 3 \times 3 = 9 \text{ inches}
\]
\[
\text{Dilated height} = 4 \times 3 = 12 \text{ inches}
\]

Next, we calculate the area of the dilated rectangle using the formula for the area of a rectangle, which is given by:

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

Substituting the dilated dimensions into this formula gives:

\[
\text{Area} = 9 \text{ inches} \times 12 \text{ inches} = 108 \text{ square inches}
\]

Therefore, the area of the dilated rectangle is

\[
\boxed{108} \text{ square inches}.
\]