To find the unknown side length (the base) in the right triangle, 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 other two sides. In this case, we have:
- Hypotenuse \( c = 30 \)
- One perpendicular side \( a = 20 \)
- The base \( b \) is unknown.
Plugging in the known values, we have:
\[ 20^2 + b^2 = 30^2 \]
Calculating \( 20^2 \) and \( 30^2 \):
\[ 400 + b^2 = 900 \]
To find \( b^2 \), subtract 400 from both sides:
\[ b^2 = 900 - 400 \] \[ b^2 = 500 \]
Now, take the square root of both sides to find \( b \):
\[ b = \sqrt{500} \] \[ b = \sqrt{100 \times 5} \] \[ b = 10\sqrt{5} \]
Now, using a calculator or looking up the value of \( \sqrt{5} \approx 2.236 \),
\[ b \approx 10 \times 2.236 \approx 22.36 \]
Thus, rounding to the nearest hundredth, the length of the unknown side (the base) is:
\[ \boxed{22.36} \]