What is the sum of the lengths, in centimeters, of the two legs of a 30-60-90 right triangle, if the length of the hypotenuse is $2\sqrt{6}$ centimeters?
<|im_start|>system
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<|im_start|>user
What is the sum of the lengths, in centimeters, of the two legs of a 30-60-90 right triangle, if the length of the hypotenuse is $2\sqrt{6}$ centimeters?
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
\sqrt{6} + 3\sqrt{2}
What is the sum of the lengths, in centimeters, of the two legs of a 30-60-90 right triangle, if the length of the hypotenuse is $2\sqrt{6}$ centimeters?
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