To find the length of the other leg of the right triangle GHI, we can use the Pythagorean theorem, which states:
\[ a^2 + b^2 = c^2 \]
where \( c \) is the length of the hypotenuse, and \( a \) and \( b \) are the lengths of the legs. In this case:
- Let \( a = 11 \) (one leg)
- Let \( b \) be the unknown leg length
- Let \( c = 22 \) (the hypotenuse)
Substituting the values into the equation gives us:
\[ 11^2 + b^2 = 22^2 \]
Calculating the squares:
\[ 121 + b^2 = 484 \]
Now, subtract 121 from both sides:
\[ b^2 = 484 - 121 \] \[ b^2 = 363 \]
Next, take the square root of both sides to find \( b \):
\[ b = \sqrt{363} \]
Calculating the square root:
\[ b \approx 19.08 \]
Thus, the length of the other leg rounded to two decimal places is:
\[ \boxed{19.08} \]