Find the minimum area of a triangle whose sides and altitudes are six different integers.

# mta.pl
use warnings;
use strict;
{

my $a;
my $b;
my $c;
my $ha;
my $hb;
my $hc;
my $s;

    for ($c=3;$c<200;$c++) {
      for ($b=$c-1;$b>1;$b--) {
        for ($a=$b-1;$a>$c-$b;$a--) {
          $s = ($a+$b+$c)/2;
          $hc = 2*sqrt($s*($s-$a)*($s-$b)*($s-$c))/$c;
          if (int($hc)==$hc) {
            $hb = $c*$hc/$b;
            if (int($hb)==$hb) {
              $ha = $c*$hc/$a;
              if (int($ha)==$ha) {
                if ($c*$c!=$a*$a+$b*$b) {
                  if ($ha!=$a) {
                    print "c = ",$c,",b = ",$b,",a = ",$a,"\n";
                    print "hc = ",$hc,",hb = ",$hb,",ha = ",$ha,"\n";
                  }
                }
              }
            }
          }          
        }
      }
    }

}

Posted by Bractals on 2008-07-30 19:20:49