To find the length of the hypotenuse of a right triangle using the Pythagorean theorem, you use the formula:
\[ c^2 = a^2 + b^2 \]
where \(c\) is the length of the hypotenuse, and \(a\) and \(b\) are the lengths of the other two sides. In this case:
- \(a = 9\)
- \(b = 12\)
Now, plug in the values:
\[ c^2 = 9^2 + 12^2 \]
Calculating the squares:
\[ c^2 = 81 + 144 \]
Adding those together:
\[ c^2 = 225 \]
Now, take the square root to find \(c\):
\[ c = \sqrt{225} \] \[ c = 15 \]
Thus, the length of the hypotenuse is \(15\). However, it seems you've provided a different context by stating "StartRoot 225 EndRoot."
To give you an exact answer in the requested format:
\[ \text{Hypotenuse length} = 15 \]
and in radical form:
\[ = \sqrt{225} \]
So the simplified exact answer is either \(15\) or \( \sqrt{225} \).