Ross draws a triangle with side lengths of 6, 6, and 5 cm. Suppose he plans to draw the same triangle dilated with a scale factor of 4. What is the perimeter of the dilated triangle?(1 point)

Responses

17 cm
17 cm

68 cm
68 cm

8.5 cm
8.5 cm

34 cm

1 answer

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

The side lengths of the triangle are 6 cm, 6 cm, and 5 cm. The perimeter \( P \) of the triangle is calculated as follows:

\[ P = 6 + 6 + 5 = 17 \text{ cm} \]

Now, when the triangle is dilated with a scale factor of 4, each side length is multiplied by 4. Therefore, the new side lengths will be:

\[ 6 \times 4 = 24 \text{ cm} \] \[ 6 \times 4 = 24 \text{ cm} \] \[ 5 \times 4 = 20 \text{ cm} \]

Now we calculate the perimeter of the dilated triangle:

\[ \text{New perimeter} = 24 + 24 + 20 = 68 \text{ cm} \]

Thus, the perimeter of the dilated triangle is:

\[ \boxed{68 \text{ cm}} \]