Answer
See explanation.
Work Step by Step
The reason is that the atmosphere is thinner at high altitude, i.e., there is lower air density and hence lower air pressure. This provides less pressure difference between the top and bottom of the wing, i.e., the effect of being at high altitude produces less lift at any given speed.
Airplanes need to land at higher speeds, which requires a longer runway to bring them to rest.
By the way, hot air is also less dense than cold air, so climate also plays a role: "high and hot" conditions generally require longer runways.
