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Plasmonic nanoantenna arrays have become increasingly popular for the detection of chemical molecules, biomolecules, viruses, and agents. In this study, our objective was to detect explosive-based 2,4-dinitrotoluene (2,4-DNT) with a metal-graphene hybrid plasmonic rectangular nanoantenna with a golden ratio size formed by choosing two consecutive numbers from the Fibonacci series. The golden rectangular resonator provides nearly perfect absorption without the need for impedance matching calculations and complex optimisation algorithms. In surface enhanced infrared absorption (SEIRA) applications, the internal losses of metallic nanostructures degrade their sensing performance. To improve performance sensitivity, graphene with high electrical conductivity and electrical tunability was used. The spectral fingerprints of 2,4 DNT at 6300 nm, 6580 nm, and 7500 nm were enhanced with a metal-graphene hybrid structure. The biosensor platform introduced, by combining the graphene and nanoantennas with a golden ratio and by adjusting the Fermi energy level of graphene, can be beneficial for highly sensitive tunable biosensors for a broad spectrum to identify the molecular fingerprints of specific biomolecules.