Source: Original.
To get some labels: Label the square ABCD, with a side length of s, where two lines leave A, there is a right angle of the internal triangle at a point on BC labeled E and an acute angle of the internal triangle on CD labeled F. Note that triangles ABE and ECF are similar. 2. If there is not integer solution to 1 then there is no integer solution to 2 since an integer solution to 2 would be a rational solution to 1 [call length AE b, EF c and FA d : so EC=sc/b, BE=s(b-c)/b, CF=sc(b-c)/b^2, FD=s(b^2-bc+c^2)/b^2] and would thus lead to an integer solution to 1 (possibly bigger).