What is the length, in units, of the shortest possible diagonal of a rectangle with all integer side lengths and perimeter 26 units? Express your answer in simplest radical form.
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
What is the length, in units, of the shortest possible diagonal of a rectangle with all integer side lengths and perimeter 26 units? Express your answer in simplest radical form.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
\sqrt{85}
What is the length, in units, of the shortest possible diagonal of a rectangle with all integer side lengths and perimeter 26 units? Express your answer in simplest radical form.
train