Is it a triangle?

Geometry Level 3

Let \(x, y\) be positive integers such that a triangle with the side lengths of \(\sqrt{25x^2+16y^2} , 2\sqrt{4x^2+y^2}, \sqrt{81x^2+4y^2} \) has area \(39\).

Find the total possible numbers of ordered pairs \( (x, y) \).

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