Let L and W be the length and width of the rectangle respectively. Then, since "the length of a rectangle is is 1 cm longer than its width," we have L = W + 1.
We know the diagonal is 4cm long. Thus, by Pythagorean's Theorem:
. . . . L<sup>2</sup> + W<sup>2</sup> = 4<sup>2</sup>
but we also know that L = W + 1, and so:
. . . . (W+1)<sup>2</sup> + W<sup>2</sup> = 4<sup>2</sup>
Now, solve for W.
edit: squared