* If you're talking about the highest mountain above sea level, then it's Mount Everest in the Himalayas, standing at 8,848.86 meters (29,031.7 feet) tall.
* If you're talking about the mountain with the greatest distance from base to peak, then it's Mauna Kea in Hawaii. While its peak is only 4,207 meters (13,796 feet) above sea level, its base is on the ocean floor, making its total height from base to peak a whopping 10,203 meters (33,474 feet) – more than twice the height of Mount Everest!
So, depending on your definition of "longest," the answer could be either Mount Everest or Mauna Kea.
