Final answer:
The child will need to take the medication for at least 6 months.
Step-by-step explanation:
The appropriate response to the mother's question about how long the child will need to take the medication is b) For at least 6 months. Isoniazid (INH) is prescribed for children with positive Mantoux tests to treat tuberculosis. The standard treatment duration for tuberculosis is usually 6 months, but it may vary depending on the severity of the infection and the patient's response to the medication.