Question

A trapezoid has a base of 10 inches, sides of 8 inches, and a top length of 4 inches. Suppose the trapezoid is dilated using a scale factor of 12
. What is the perimeter of the dilated trapezoid?(1 point)
Responses

60 inches
60 inches

15 inches
15 inches

11 inches
11 inches

30 inches

Answer 1

To find the perimeter of the dilated trapezoid, we first need to calculate the original perimeter of the trapezoid.

The perimeter \( P \) of the original trapezoid can be calculated using the lengths of all sides:

\[
P = \text{base} + \text{side 1} + \text{side 2} + \text{top}
\]

Plugging in the values:

\[
P = 10 \text{ inches} + 8 \text{ inches} + 8 \text{ inches} + 4 \text{ inches} = 10 + 8 + 8 + 4 = 30 \text{ inches}
\]

Next, we apply the dilation with a scale factor of 12. The new perimeter \( P' \) of the dilated trapezoid will be:

\[
P' = \text{scale factor} \times P = 12 \times 30 \text{ inches} = 360 \text{ inches}
\]

None of the responses listed match this calculation exactly.

However, if the problem only requires the perimeter of the original trapezoid rather than the dilated one, the perimeter remains at:

\[
30 \text{ inches}
\]

Thus, if the question is strictly about the original trapezoid and clarifies nothing about dilation, the perimeter is \( 30 \) inches. If it's indeed asking about the perimeter post-dilation, it would be \( 360 \) inches, which is not provided in the options.

If you have to choose from the available responses regarding the original trapezoid, the answer is:

**30 inches.**