The sides of a right triangle are $a$ and $b$, and the hypotenuse is $c$. A perpendicular from the vertex divides $c$ into segments $r$ and $s$, adjacent respectively to $a$ and $b$. If $a : b = 1 : 3$, find the ratio of $r$ to $s$. The original answer is in the format of k:m, please give the value of k + m.

Let's think step by step and output the final answer within \boxed{}.
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