Final answer:
The patient, presenting symptoms of hyperglycemia and destroyed pancreatic beta cells, would be diagnosed with Type 1 diabetes, an autoimmune condition commonly diagnosed in young people that requires insulin administration for management.
Step-by-step explanation:
The correct diagnosis for a 15-year-old child presenting with symptoms of hyperglycemia and with destroyed pancreatic beta cells is Type 1 diabetes (also known as Juvenile diabetes).
Type 1 diabetes is an autoimmune disorder where the immune system erroneously attacks and destroys the beta cells in the pancreas that are responsible for producing insulin. This leads to a lack of insulin and causes high blood glucose levels or hyperglycemia. The disease can occur at any age, but it is most commonly diagnosed in children, adolescents, and young adults. Symptoms like excessive urination, thirst, weight loss, and fatigue usually have a sudden onset. Managing type 1 diabetes necessitates the administration of synthetic insulin through injections or an insulin pump.
In contrast, Type 2 diabetes usually develops due to a combination of environmental and genetic factors leading to insulin resistance and is more commonly diagnosed in adults, though it is increasingly observed in children and adolescents as well. However, Type 2 diabetes does not involve an autoimmune destruction of beta cells.