Question 1105434
Not sure if you are missing information about your "third side" or not.


Sides are these:
x, shortest side, 
m+2x, hypotenuse
(m+2x)-1, third side, "meter less than the hypotenuse"


Right triangle, Pythagorean Theorem, because one of the sides is a "hypotenuse".
{{{x^2+(2x+m-1)^2=(2x+m)^2}}}

Two unknown variables but just one single equation.


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{{{x^2+(2x+m)^2-4x-2m+1=4x^2+4mx+m^2}}}
{{{x^2+4x^2+4mx+m^2-4x-2m+1=4x^2+4mx+m^2}}}
{{{x^2-4x-2m+1=0}}}
Still one equation in two unknown variables.  Maybe use of discriminant may give some more information possible about m ?