Final answer:
The locus of points inside the rectangle that are 3cm away from its sides is a smaller rectangle with dimensions 2cm by 1cm.
Step-by-step explanation:
The locus of points inside the rectangle PQRS that are 3cm away from PQ, QR, RS, and SP can be found by constructing circles centered at each of the vertices of the rectangle with a radius of 3cm. The locus of points inside the rectangle that are equidistant from its sides will be the region enclosed by the arcs of these circles. This region is a smaller rectangle with dimensions 2cm by 1cm.