Final answer:
Menendez maintained Spanish control in Florida through alliances with Native American tribes, the establishment of mission villages, and military fortifications to defend against other European powers.
Step-by-step explanation:
Menendez was able to keep Florida under Spanish control for many years primarily by forming alliances with Native American tribes and establishing a strong military presence. These alliances, particularly with tribes like the Guale, Timucua, and Apalachee, were fortified through the establishment of a chain of religious mission villages which served to Christianize, acculturate, and integrate the indigenous population as a part of the Spanish colonial enterprise. In addition to this, the Spanish built fortifications, like the Castillo de San Marcos, which served to defend against imperial challengers and to protect Spanish interests in the region.
The combination of these diplomatic and military strategies helped to maintain Spanish control over Florida for an extended period, amidst growing challenges from other European powers and Native American groups.