2006 iTest Problems/Problem U7: Difference between revisions
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==Problem== | ==Problem== | ||
Let <math>T = TNFTPP</math>. Triangle <math>ABC</math> has integer side lengths, including <math>BC = | Let <math>T = TNFTPP</math>. 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 20:37, 17 November 2019
Problem
Let 
. 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
