With recent developments in the search for novel device ideas, understanding electron-electron interaction in low dimensional systems is of particular interest. Coulomb drag measurements can provide critical insights in this context. In this article, we present a novel planar graphene double ribbon structure that shows for the first time that Coulomb drag is observable in two adjacent monolayer ribbons in the same plane at room temperature. Moreover, our planar devices enable experimentally study of the impact of the dielectric constant on Coulomb drag which is difficult to explore in the typically used double layer graphene structures. Our experimental findings indicate in particular that the drag resistance is proportional to the dielectric constant (ε) and does not, as recently reported, show an increasing trend of interaction strength for small ε-values. In fact, we find that the drag resistance follows approximately an ε 1.2-dependence. The exponent of "1.2" is consistent with the theory considering the carrier concentration in our samples, and positions our results in between the weak and strong coupling limits.