To find the length \( s \) of the long piece of string before Diana cuts it, we need to consider that she cuts the string into 8 equal pieces, each being 1.25 feet long.
The relationship can be expressed with the equation:
\[ s = 8 \times 1.25 \]
Now, we can solve this equation:
\[ s = 8 \times 1.25 \]
Calculating the right side:
\[ 8 \times 1.25 = 10 \]
So,
\[ s = 10 \text{ feet} \]
Thus, the length of the long piece of string before Diana cuts it is 10 feet.