Final answer:
President George W. Bush declared a war on terror following the September 11, 2001 attacks to eliminate Al-Qaeda and prevent future attacks.
Step-by-step explanation:
President George W. Bush declared a war on terror following the September 11, 2001 attacks because the attacks were orchestrated by the terrorist organization Al-Qaeda, led by Osama bin Laden. The attacks resulted in the deaths of nearly 3,000 people and were significant in their scale and impact on the United States. By declaring a war on terror, President Bush aimed to eliminate Al-Qaeda and other associated militant organizations in order to prevent future attacks.