Dilate a square with vertices $\left(0,\ 0\right)$(0, 0)​ , $\left(0,\ 4\right)$(0, 4)​ , $\left(4,\ 4\right)$(4, 4)​ , and $\left(4,\ 0\right)$(4, 0)​ using the scale factor $k=0.5$k=0.5​ . What is the value of the ratio (new to original) of the perimeters? the areas?