Final answer:
Based on the child's symptoms and vital signs, the child likely requires fluid resuscitation at a rate of 36 mL per hour.
Step-by-step explanation:
Based on the given information, the child is showing signs of dehydration and shock due to the symptoms of fever, vomiting, and diarrhea. The vital signs such as increased heart rate (HR 190), reduced blood pressure (BP 59/29), and mottled extremities indicate poor perfusion and decreased circulating volume. Given the weight of 6 kg, the child will likely require fluid resuscitation.
The fluid requirements for a dehydrated child can be calculated using the Parkland formula:
Fluid requirements = weight in kg × % body surface area burned × 4 (mL)
Since the child has symptoms of dehydration, it is assumed that a significant portion of the body is affected, so a % body surface area burned of 15% can be used. Using the formula:
Fluid requirements = 6 kg × 15% × 4 mL = 36 mL per hour
Therefore, this child requires a fluid resuscitation rate of 36 mL per hour.