Difference between revisions of "2006 iTest Problems/Problem U7"

(Created page with "==Problem== Let <math>T = TNFTPP</math>. Triangle <math>ABC</math> has integer side lengths, including <math>BC = 100T - 4</math>, and a right angle, <math>\angle A...")
 
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==Solution==
 
==Solution==
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First, label the other leg <math>x</math> and the hypotenuse <math>y</math>. To minimize

Revision as of 21:37, 17 November 2019

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

First, label the other leg $x$ and the hypotenuse $y$. To minimize

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