Higher density altitude leads to takeoff distance:

• A. Longer
• B. Shorter
• C. Unchanged
• D. Depends on wind

Answer: (A)

Higher density altitude means the air is thinner. When the air is thinner, the wings generate less lift at the same speed, and engines/propellers develop less thrust because there are fewer air molecules to work with. Because of this, you need to accelerate to a higher true airspeed to get enough lift and thrust for rotation and liftoff. That extra speed takes more runway, so the takeoff distance increases.

Wind can change the actual distance you measure on the ground (a headwind can shorten the ground roll, a tailwind can lengthen it), but the fundamental effect of thinner air is to require more runway overall.