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

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==Problem== | ==Problem== | ||

− | + | Triangle <math>ABC</math> has integer side lengths, including <math>BC = 696</math>, and a right angle, <math>\angle ABC</math>. Let <math>r</math> and <math>s</math> denote the inradius and semiperimeter of <math>ABC</math> respectively. Find the perimeter of the triangle ABC which minimizes <math>\frac{s}{r}</math>. | |

==Solution== | ==Solution== | ||

First, label the other leg <math>x</math> and the hypotenuse <math>y</math>. To minimize | First, label the other leg <math>x</math> and the hypotenuse <math>y</math>. To minimize |

## Revision as of 21:39, 17 November 2019

## Problem

Triangle has integer side lengths, including , and a right angle, . Let and denote the inradius and semiperimeter of respectively. Find the perimeter of the triangle ABC which minimizes .

## Solution

First, label the other leg and the hypotenuse . To minimize