Question

7cm
25cm
24cm
Suppose the triangle in the diagram was dilated using a scale factor of 2. What is the perimeter of the dilated triangle?

(1 point)
Responses

56 cm
56 cm

112 cm
112 cm

28 cm
28 cm

168 cm

Answer 1

To find the perimeter of the dilated triangle, first calculate the perimeter of the original triangle.

The sides of the original triangle are:
- 7 cm
- 25 cm
- 24 cm

Calculate the perimeter of the original triangle:

\[
\text{Perimeter} = 7 \, \text{cm} + 25 \, \text{cm} + 24 \, \text{cm} = 56 \, \text{cm}
\]

Now, since the triangle is dilated using a scale factor of 2, each side of the triangle is multiplied by 2. Therefore, the sides of the dilated triangle will be:

- \(7 \, \text{cm} \times 2 = 14 \, \text{cm}\)
- \(25 \, \text{cm} \times 2 = 50 \, \text{cm}\)
- \(24 \, \text{cm} \times 2 = 48 \, \text{cm}\)

Now, calculate the perimeter of the dilated triangle:

\[
\text{Perimeter of dilated triangle} = 14 \, \text{cm} + 50 \, \text{cm} + 48 \, \text{cm} = 112 \, \text{cm}
\]

So, the perimeter of the dilated triangle is **112 cm**.