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

Question

. 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 $P^{\prime }$ of the dilated trapezoid will be:

$$P^{\prime }=\text{scale factor}\times P=12\times 30\text{ inches}=360\text{ inches}$$

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.