1.  Make a sketch.
    Let ABC be your right-angled triangle with the right angle vertex A.
    Let BD and CE be these two medians (|CE| = 2*sqrt(13) and |BD| = sqrt(73), for certainty).
    Let x and y be the lengths of the legs AB and AC respectively.


2.  From the right triangle ACE and ABD you have

     =    (1)

     =    (2)

or

     =      (3)

     = ,      (4)

By adding equations (3) and (4), you get

     = 4*13 + 73 = 125,   or

     = 100.


3.  Thus  = 100.

    It is the length of the hypotenuse squared, .

    Hence, the length of the hypotenuse  =  = 10 cm.