number theory - Perfect Squares: relatively prime and increasing arithmetic progression

The squares 1, 25, 49 are pairwise relatively prime and in an increasing arithmetic progression. Let $x_1^2, y_1^2, z_1^2$ and $x_2^2, y_2^2, z_2^2$ be the next two triples with this property (so that 49, $z_1^2$, $z_2^2$ are the three smallest possible values of the third term). Find $z_1 + z_2$.

I really help about how to start/a good solution for this problem because I understand what the problem is asking but I'm not sure how to start. Thanks!