How many units are in the sum of the lengths of the three altitudes in a triangle with sides $7,$ $24,$ and $25$? Express your answer as a decimal to the nearest hundredth.
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
How many units are in the sum of the lengths of the three altitudes in a triangle with sides $7,$ $24,$ and $25$? Express your answer as a decimal to the nearest hundredth.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
37.72
How many units are in the sum of the lengths of the three altitudes in a triangle with sides $7,$ $24,$ and $25$? Express your answer as a decimal to the nearest hundredth.
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