how to find all possible sides of a triangle when the area is given

This is not a programming task but rather a geometrical problem.
Knowing that all triangles with a given base side and a given height have the same area, you can chose for a given area an arbitrary base side and have the adjacent point sweep from infinite left to infinite right on a parallel of height distance to the baes line, always maintaining the same area (two times the area = base length times hight). This gives infinte number of sides for each arbitrarily chosen base line.

So, the question is, if there are further constraints. If not, you have infinite number of sides and even worse, some two sides may become infinite, even for a finite area.

Cheers
Andi

PS: There may for a given area be no or many solutions for integral numbers.

My best bet would be Herons Formula[^]

for (a=1;a<=s;a++{
        for(b=1;b<=s;b++){
            for(c=1;c<=s;c++){
                if((a+b>c)&&(b+c>a)&&(c+a>b)){
               k=(a+b+c)%2;
                if(k==0){
                   p=(a+b+c)/2.0;
                    s1=sqrt(p*(p-a)*(p-b)*(p-c));

if(s==s1)
print