so hmmm if you look at the picture below
the lenght of the rectangle, is really just 4 radius worth, or 2 diameters for that matter, and the width of the rectangle is 1 diameter worth, or 2 radius, so the perimeter of the rectangle containing the circles is really just 2r + 2r + 4r + 4r, or just 12r.
we know the area of each circle is 196π, thus
[tex]\bf \textit{area of a circle}\\\\ A=\pi r^2~~ \begin{cases} r=radius\\ \cline{1-1} A=196\pi \end{cases}\implies 196\pi =\pi r^2\implies \cfrac{196\pi }{\pi }=r^2 \\\\\\ 196=r^2\implies \sqrt{196}=r\implies 14=r \\\\[-0.35em] ~\dotfill\\\\ ~\hfill \stackrel{\textit{perimeter of the rectangle}}{12r\implies 12(14)\implies 168}~\hfill[/tex]
