Note that a polygon decomposed into $m$ triangles can contain at most $3m$ sides. It is easy enough to construct a $3m$-gon out of $m$ right isosceles triangles; start with one right isosceles triangle, stick another one onto it with two base sides overlapping, but with distinct endpoints; continue in this fashion for all $m$ triangles. It is trivial to make all the sides unequal. Since a right isosceles triangle can be decomposed into any number of right isosceles triangles, we have a decomposition into $k$ triangles for all $k\geq m$. For a polygon with $3m+1$ sides, first we form a triangle with 4 sides by sticking two right isosceles triangles together so that two of the sides form one long side; the other base sides should be unequal, so that there are four sides. Then the construction is continued as above, forming $3m+1$ sides after $m+1$ triangles are added. For a polygon with $3m+2$ sides, place two right isosceles triangles together so that they share a vertex, but the nonoverlapping sides are not parallel; this gives five sides. Again, continue the construction as before. In both cases, it is trivial to make all sides unequal. So whenever an $n$-polygon can be decomposed into $m$ triangles, it is possible to construct an $n$-polygon with unequal sides out of $m$ right isosceles triangles.