2006 iTest Problems/Problem U7

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Problem

Let $T  =  TNFTPP$. Triangle $ABC$ has integer side lengths, including $BC  =  100T  -  4$, and a right angle, $\angle ABC$. Let $r$ and $s$ denote the inradius and semiperimeter of $ABC$ respectively. Find the perimeter of the triangle ABC which minimizes $\frac{s}{r}$.

Solution

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