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 determine the perimeter of the original trapezoid before dilation.

The perimeter \( P \) of a trapezoid is calculated as the sum of the lengths of all its sides. For the given trapezoid:

- Base 1 (bottom base) = 10 inches
- Base 2 (top base) = 4 inches
- Side 1 = 8 inches
- Side 2 = 8 inches

Now, we can find the perimeter of the original trapezoid:

\[
P = \text{Base 1} + \text{Base 2} + \text{Side 1} + \text{Side 2}
\]
\[
P = 10 + 4 + 8 + 8
\]
\[
P = 30 \text{ inches}
\]

Since the trapezoid is dilated with a scale factor of 12, the perimeter of the dilated trapezoid will be 12 times the perimeter of the original trapezoid:

\[
\text{Perimeter of dilated trapezoid} = 12 \times P
\]
\[
\text{Perimeter of dilated trapezoid} = 12 \times 30
\]
\[
\text{Perimeter of dilated trapezoid} = 360 \text{ inches}
\]

However, 360 inches is not one of the options provided. The original perimeter of 30 inches multiplied by the scale factor of 12 gives us 360 inches, which suggests that the answer does not match any of the provided options.

Please check the problem or provide the correct options, as the calculated perimeter of the dilated trapezoid is indeed 360 inches.