Final answer:
Children with epiglottitis often exhibit difficulty breathing or swallowing, which indicates the need for a tracheotomy to secure the airway.
Step-by-step explanation:
Behavior that would indicate the need for a tracheotomy in a child with epiglottitis is b) Difficulty breathing or swallowing. The larynx, including the epiglottis, plays a critical role in ensuring that food and other swallowed materials do not enter the respiratory tract. When the epiglottis is inflamed during epiglottitis, it can fail to protect effectively, leading to severe breathing difficulties due to airway obstruction. Respiratory symptoms such as shortness of breath, wheezing or stridor, and hoarseness are common. A tracheotomy may become necessary to bypass the obstructed airway and provide a secure route for breathing.