The area of a shape that has been dilated by a scale factor \( k \) changes by a factor of \( k^2 \). This means that if the area of the dilated triangle is 6.25 times the area of the original triangle, we can set up the equation:
\[ k^2 = 6.25 \]
To find the scale factor \( k \), we take the square root of both sides:
\[ k = \sqrt{6.25} \]
Calculating the square root:
\[ k = 2.5 \]
Thus, the scale factor for the dilation is \( 2.5 \).