Context. Periodicities have frequently been reported across many wavelengths in the solar corona. Correlated periods of ~5 min, comparable to solar p-modes, are suggestive of coupling between the photosphere and the corona. Aims. Our study investigates whether there are correlations in the periodic behavior of Type III radio bursts which are indicative of nonthermal electron acceleration processes, and coronal extreme ultraviolet (EUV) emission used to assess heating and cooling in an active region when there are no large flares. Methods. We used coordinated observations of Type III radio bursts from the FIELDS instrument on Parker Solar Probe (PSP), of EUV emissions by the Solar Dynamics Observatory (SDO) Atmospheric Imaging Assembly (AIA) and white light observations by SDO Helioseismic and Magnetic Image (HMI), and of solar flare X-rays by Nuclear Spectroscopic Telescope Array (NuSTAR) on April 12, 2019. Several methods for assessing periodicities are utilized and compared to validate periods obtained. Results. Periodicities of ~5 min in the EUV in several areas of an active region are well correlated with the repetition rate of the Type III radio bursts observed on both PSP and Wind. Detrended 211 and 171 Å light curves show periodic profiles in multiple locations, with 171 Å peaks sometimes lagging those seen in 211 Å. This is suggestive of impulsive events that result in heating and then cooling in the lower corona. NuSTAR X-rays provide evidence for at least one microflare during the interval of Type III bursts, but there is not a one-to-one correspondence between the X-rays and the Type III bursts. Our study provides evidence for periodic acceleration of nonthermal electrons (required to generate Type III radio bursts) when there were no observable flares either in the X-ray data or the EUV. The acceleration process, therefore, must be associated with small impulsive events, perhaps nanoflares.