All the triangles are similar, so
.. short side/long side = 9/x = x/25
.. x^2 = 9*25 . . . . . . "cross multiply"
.. x = 3*5 . . . . . . . . . square root*
.. x = 15
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* Since these are lengths of line segments, they are non-negative numbers. We can ignore the negative square root.