The edge of the new cube formed by combining three cubes with edges measuring 3cm, 4cm, and 5cm respectively is 6cm.
To form a single cube from three smaller cubes, each with edges measuring 3cm, 4cm, and 5cm, we can combine them in a way that aligns their vertices. The largest cube will have a diagonal along one of its face diagonals, connecting opposite corners. For a cube with edges of 3cm, 4cm, and 5cm, the diagonal of the face formed by the 3cm and 4cm edges will have a length of 5cm according to the Pythagorean theorem.
Now, when aligning three cubes along their diagonals, the new cube's edges will be the sum of the edges of the individual cubes along the common diagonal. Therefore, the edge of the new cube will be 3cm + 4cm + 5cm = 12cm. The resulting cube has all edges measuring 12cm, forming a single cube from the smaller ones.