In a 30-60-90 triangle, the lengths of the sides are in the ratio 1 : √3 : 2. This means:
- The side opposite the 30-degree angle is the shortest and is \(x\).
- The side opposite the 60-degree angle (which is the given length) is \(x\sqrt{3}\).
- The hypotenuse (opposite the 90-degree angle) is \(2x\).
Given that the side opposite the 60-degree angle is \(6\sqrt{3}\):
\[ x\sqrt{3} = 6\sqrt{3} \]
To find \(x\), divide both sides by \(\sqrt{3}\):
\[ x = 6 \]
Now, we can find the hypotenuse:
\[ \text{Hypotenuse} = 2x = 2(6) = 12 \]
Therefore, the length of the hypotenuse is \(\boxed{12}\).
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