Area and Perimeter under Dilation

Scale every length by $k$ and the consequences are fixed: perimeter scales by $k$, area by $k^2$, volume by $k^3$.

A 4 by 8 inch picture enlarged to 12 by 24 inches has $k = 3$, so its perimeter triples and its area grows ninefold.

The trap is answering with $k^2$ when the question asked about perimeter. Read which quantity is being scaled before computing anything.