To find the length of the other leg in the right triangle GHI, we can use the Pythagorean theorem. The theorem states that for a right triangle with legs \( a \) and \( b \), and hypotenuse \( c \):
\[ a^2 + b^2 = c^2 \]
In this case, we know one leg \( a = 11 \) and the hypotenuse \( c = 22 \). We need to find the length of the other leg \( b \).
First, we substitute the known values into the Pythagorean theorem:
\[ 11^2 + b^2 = 22^2 \]
Calculating each square:
\[ 121 + b^2 = 484 \]
Next, we isolate \( b^2 \):
\[ b^2 = 484 - 121 \]
Calculating the right-hand side:
\[ b^2 = 363 \]
Now, we find \( b \) by taking the square root of both sides:
\[ b = \sqrt{363} \]
Using a calculator to compute \( \sqrt{363} \):
\[ b \approx 19.1 \]
Thus, the length of the other leg, rounded to two decimal places, is:
\[ \boxed{19.10} \]