To find the perimeter of the dilated triangle, we first need to determine the perimeter of the original triangle. The side lengths of the original triangle are 6 cm, 6 cm, and 5 cm.
We can calculate the perimeter \( P \) of the original triangle:
\[ P = 6 + 6 + 5 = 17 \text{ cm} \]
Next, Ross plans to dilate the triangle with a scale factor of 4. When a triangle is dilated, each side length is multiplied by the scale factor. Therefore, the side lengths of the dilated triangle will be:
- Side 1: \( 6 \times 4 = 24 \) cm
- Side 2: \( 6 \times 4 = 24 \) cm
- Side 3: \( 5 \times 4 = 20 \) cm
Now we can calculate the perimeter \( P' \) of the dilated triangle:
\[ P' = 24 + 24 + 20 \]
Calculating this gives:
\[ P' = 48 + 20 = 68 \text{ cm} \]
Thus, the perimeter of the dilated triangle is \(\boxed{68}\) cm.