Python3, 257 bytes

lambda:[(m,n,r)for m in range(1,101)for n in range(m+1,101)for r in range(1,101)if F(n,m,r)and m+n<2*r]
def F(n,m,r):
 T=r**2-((n+m)/2)**2
 if T<0:return 0
 L=2*T**.5
 U=abs((-L+(L**2+4*m*n)**.5)/2)
 return U and int(U)==U and sorted([U,L+U])!=sorted([n,m])

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