To find the perimeter of the dilated triangle, we first calculate the perimeter of the original triangle. Given a right triangle with leg lengths of 7 and 24, and a hypotenuse of 25, we calculate the perimeter as follows:
\[ \text{Perimeter}_{\text{original}} = 7 + 24 + 25 = 56 \]
Next, when the triangle is dilated using a scale factor of 2, all side lengths are multiplied by 2. Thus, the new leg lengths and hypotenuse are:
\[ \text{New leg length 1} = 7 \times 2 = 14 \] \[ \text{New leg length 2} = 24 \times 2 = 48 \] \[ \text{New hypotenuse} = 25 \times 2 = 50 \]
Now, we find the perimeter of the dilated triangle:
\[ \text{Perimeter}_{\text{dilated}} = 14 + 48 + 50 \]
Calculating this:
\[ 14 + 48 = 62 \] \[ 62 + 50 = 112 \]
Thus, the perimeter of the dilated triangle is \( \boxed{112} \).