To find the unknown side length \( x \) in the triangle, we start with the given equation:
\[ 20^2 + x^2 = 30^2 \]
Calculating the squares:
\[ 20^2 = 400 \] \[ 30^2 = 900 \]
Substituting these values into the equation gives:
\[ 400 + x^2 = 900 \]
Next, we isolate \( x^2 \) by subtracting 400 from both sides:
\[ x^2 = 900 - 400 \] \[ x^2 = 500 \]
Now, we take the square root of both sides to find \( x \):
\[ x = \sqrt{500} \]
Simplifying \( \sqrt{500} \):
\[ \sqrt{500} = \sqrt{100 \times 5} = \sqrt{100} \times \sqrt{5} = 10\sqrt{5} \]
Now, using the approximate value of \( \sqrt{5} \approx 2.236 \):
\[ x \approx 10 \times 2.236 = 22.36 \]
Thus, rounding to the nearest hundredth, the length of the unknown side \( x \) is:
\[ \boxed{22.36} \]